<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-03235536v2</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-11T03:40:28+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Reduction for branching multiplicities</title>
            <author role="aut">
              <persName>
                <forename type="first">Pierre-Emmanuel</forename>
                <surname>Chaput</surname>
              </persName>
              <email type="md5">44d07b944377d81ca5d0150e94016070</email>
              <email type="domain">univ-lorraine.fr</email>
              <idno type="idhal" notation="string">pechaput</idno>
              <idno type="idhal" notation="numeric">3420</idno>
              <idno type="halauthorid" notation="string">1063-3420</idno>
              <idno type="IDREF">https://www.idref.fr/106958917</idno>
              <affiliation ref="#struct-211251"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Nicolas</forename>
                <surname>Ressayre</surname>
              </persName>
              <email type="md5">605986b2426e1c304cde1df8925f8841</email>
              <email type="domain">math.univ-lyon1.fr</email>
              <idno type="idhal" notation="string">nicolas-ressayre</idno>
              <idno type="idhal" notation="numeric">173206</idno>
              <idno type="halauthorid" notation="string">1636-173206</idno>
              <idno type="IDREF">https://www.idref.fr/050150294</idno>
              <affiliation ref="#struct-193738"/>
              <affiliation ref="#struct-521750"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Pierre-Emmanuel</forename>
                <surname>Chaput</surname>
              </persName>
              <email type="md5">44d07b944377d81ca5d0150e94016070</email>
              <email type="domain">univ-lorraine.fr</email>
            </editor>
            <funder ref="#projanr-41932"/>
          </titleStmt>
          <editionStmt>
            <edition n="v1">
              <date type="whenSubmitted">2021-05-25 18:47:42</date>
            </edition>
            <edition n="v2" type="current">
              <date type="whenSubmitted">2022-04-08 15:05:09</date>
              <date type="whenModified">2026-04-23 14:50:05</date>
              <date type="whenReleased">2022-04-11 11:43:30</date>
              <date type="whenProduced">2022-09-15</date>
              <date type="whenEndEmbargoed">2022-04-08</date>
              <ref type="file" target="https://hal.science/hal-03235536v2/document">
                <date notBefore="2022-04-08"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-03235536v2/file/multiplicity_v2.pdf" id="file-3635484-3176229">
                <date notBefore="2022-04-08"/>
                <desc>Ce pdf est la version preprint de l'article (version soumise à l'éditeur, avant peer-reviewing)</desc>
              </ref>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="311923">
                <persName>
                  <forename>Pierre-Emmanuel</forename>
                  <surname>Chaput</surname>
                </persName>
                <email type="md5">44d07b944377d81ca5d0150e94016070</email>
                <email type="domain">univ-lorraine.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-03235536</idno>
            <idno type="halUri">https://hal.science/hal-03235536</idno>
            <idno type="halBibtex">chaput:hal-03235536</idno>
            <idno type="halRefHtml">&lt;i&gt;International Mathematics Research Notices&lt;/i&gt;, 2022, &lt;a target="_blank" href="https://dx.doi.org/10.1093/imrn/rnac248"&gt;&amp;#x27E8;10.1093/imrn/rnac248&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">International Mathematics Research Notices, 2022, &amp;#x27E8;10.1093/imrn/rnac248&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-3635484-3176229"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="UNIV-ST-ETIENNE">Université Jean Monnet - Saint-Etienne</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="ICJ" corresp="UNIV-LYON1">Institut Camille Jordan</idno>
            <idno type="stamp" n="UNIV-LYON1">Université Claude Bernard - Lyon I</idno>
            <idno type="stamp" n="INSA-LYON">Institut National des Sciences Appliquées de Lyon</idno>
            <idno type="stamp" n="EC-LYON">Ecole Centrale de Lyon</idno>
            <idno type="stamp" n="IECN">IECL - Institut Elie Cartan de Lorraine</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="UNIV-LORRAINE">Université de Lorraine</idno>
            <idno type="stamp" n="IECLGEO">Géométrie</idno>
            <idno type="stamp" n="INSA-GROUPE">Groupe INSA</idno>
            <idno type="stamp" n="UDL">UDL</idno>
            <idno type="stamp" n="UNIV-LYON">Université de Lyon</idno>
            <idno type="stamp" n="ANR">ANR</idno>
            <idno type="stamp" n="AM2I-UL">Pôle scientifique Automatique, Mathématiques, Informatique et leurs Intéractions de l'Université de Lorraine</idno>
            <idno type="stamp" n="ANR_QUANTIQUE">ANR QUANTIQUE</idno>
            <idno type="stamp" n="ANR_QUANTIQUE_3" corresp="ANR_QUANTIQUE">ANR_QUANTIQUE_3</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Reduction for branching multiplicities</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Pierre-Emmanuel</forename>
                    <surname>Chaput</surname>
                  </persName>
                  <email type="md5">44d07b944377d81ca5d0150e94016070</email>
                  <email type="domain">univ-lorraine.fr</email>
                  <idno type="idhal" notation="string">pechaput</idno>
                  <idno type="idhal" notation="numeric">3420</idno>
                  <idno type="halauthorid" notation="string">1063-3420</idno>
                  <idno type="IDREF">https://www.idref.fr/106958917</idno>
                  <affiliation ref="#struct-211251"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Nicolas</forename>
                    <surname>Ressayre</surname>
                  </persName>
                  <email type="md5">605986b2426e1c304cde1df8925f8841</email>
                  <email type="domain">math.univ-lyon1.fr</email>
                  <idno type="idhal" notation="string">nicolas-ressayre</idno>
                  <idno type="idhal" notation="numeric">173206</idno>
                  <idno type="halauthorid" notation="string">1636-173206</idno>
                  <idno type="IDREF">https://www.idref.fr/050150294</idno>
                  <affiliation ref="#struct-193738"/>
                  <affiliation ref="#struct-521750"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">14787</idno>
                <idno type="issn">1073-7928</idno>
                <idno type="eissn">1687-0247</idno>
                <title level="j">International Mathematics Research Notices</title>
                <imprint>
                  <publisher>Oxford University Press (OUP)</publisher>
                  <date type="datePub">2022-09-15</date>
                </imprint>
              </monogr>
              <idno type="doi">10.1093/imrn/rnac248</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <classCode scheme="halDomain" n="math.math-ag">Mathematics [math]/Algebraic Geometry [math.AG]</classCode>
              <classCode scheme="halDomain" n="math.math-rt">Mathematics [math]/Representation Theory [math.RT]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>A reduction formula for the branching coefficients of tensor products of representations and more generally restrictions of representations of a semisimple group to a semisimple subgroup is proved in [KT03, DW11]. This formula holds when the highest weights of the representations belong to a codimension 1 face of the Horn cone, which by [Res11b] corresponds to a Littlewood-Richardson coefficient equal to 1. We prove a similar reduction formula when this coefficient is equal to 2, and show some properties of the class of the branch divisor corresponding to a generically finite morphism of degree 2 naturally defined in this context.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-211251" status="VALID">
          <idno type="IdRef">180064606</idno>
          <idno type="ISNI">0000000120974820</idno>
          <idno type="RNSR">199712570F</idno>
          <idno type="IdUnivLorraine">[UL]RSB--</idno>
          <idno type="ROR">https://ror.org/04rvw8791</idno>
          <orgName>Institut Élie Cartan de Lorraine</orgName>
          <orgName type="acronym">IECL</orgName>
          <date type="start">2013-01-01</date>
          <desc>
            <address>
              <addrLine>Université de Lorraine, Boulevard des Aiguillettes BP 70239 54506 Vandoeuvre-les-Nancy CedexIle du Saulcy - 57 045 Metz Cedex 01</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://iecl.univ-lorraine.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-413289" type="direct"/>
            <relation name="UMR7502" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-193738" status="VALID">
          <idno type="IdRef">111872227</idno>
          <idno type="ISNI">0000000403832988</idno>
          <idno type="RNSR">200511878U</idno>
          <idno type="ROR">https://ror.org/01ekw7f87</idno>
          <orgName>Institut Camille Jordan</orgName>
          <orgName type="acronym">ICJ</orgName>
          <date type="start">2005-01-01</date>
          <desc>
            <address>
              <addrLine>Bât. Jean Braconnier 43 bd du 11 novembre 1918 69622 VILLEURBANNE CEDEX</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://math.univ-lyon1.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-126765" type="direct"/>
            <relation active="#struct-301088" type="indirect"/>
            <relation active="#struct-194495" type="direct"/>
            <relation active="#struct-219748" type="direct"/>
            <relation active="#struct-301232" type="indirect"/>
            <relation active="#struct-300284" type="direct"/>
            <relation active="#struct-1327915" type="indirect"/>
            <relation name="UMR5208" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="researchteam" xml:id="struct-521750" status="VALID">
          <orgName>Algèbre, géométrie, logique</orgName>
          <orgName type="acronym">AGL</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">http://math.univ-lyon1.fr/spip.php?article8</ref>
          </desc>
          <listRelation>
            <relation active="#struct-193738" type="direct"/>
            <relation active="#struct-126765" type="indirect"/>
            <relation active="#struct-301088" type="indirect"/>
            <relation active="#struct-194495" type="indirect"/>
            <relation active="#struct-219748" type="indirect"/>
            <relation active="#struct-301232" type="indirect"/>
            <relation active="#struct-300284" type="indirect"/>
            <relation active="#struct-1327915" type="indirect"/>
            <relation name="UMR5208" active="#struct-441569" type="indirect"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-413289" status="VALID">
          <idno type="IdRef">157040569</idno>
          <idno type="IdUnivLorraine">[UL]100--</idno>
          <idno type="ROR">https://ror.org/04vfs2w97</idno>
          <orgName>Université de Lorraine</orgName>
          <orgName type="acronym">UL</orgName>
          <date type="start">2012-01-01</date>
          <desc>
            <address>
              <addrLine>34 cours Léopold - CS 25233 - 54052 Nancy cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-lorraine.fr/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-126765" status="VALID">
          <idno type="ROR">https://ror.org/05s6rge65</idno>
          <orgName>École Centrale de Lyon</orgName>
          <orgName type="acronym">ECL</orgName>
          <desc>
            <address>
              <addrLine>36 avenue Guy de Collongue - 69134 Ecully cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.ec-lyon.fr</ref>
          </desc>
          <listRelation>
            <relation active="#struct-301088" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-301088" status="VALID">
          <idno type="ROR">https://ror.org/01rk35k63</idno>
          <orgName>Université de Lyon</orgName>
          <desc>
            <address>
              <addrLine>92 rue Pasteur - CS 30122, 69361 Lyon Cedex 07</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.universite-lyon.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-194495" status="VALID">
          <idno type="IdRef">026402823</idno>
          <idno type="ISNI">0000000121686185</idno>
          <idno type="ROR">https://ror.org/029brtt94</idno>
          <orgName>Université Claude Bernard Lyon 1</orgName>
          <orgName type="acronym">UCBL</orgName>
          <desc>
            <address>
              <addrLine>43, boulevard du 11 novembre 1918, 69622 Villeurbanne cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-lyon1.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-301088" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-219748" status="VALID">
          <idno type="IdRef">052444724</idno>
          <idno type="ISNI">0000 0001 2292 0228</idno>
          <orgName>Institut National des Sciences Appliquées de Lyon</orgName>
          <orgName type="acronym">INSA Lyon</orgName>
          <date type="start">1957-03-18</date>
          <desc>
            <address>
              <addrLine>20 Avenue Albert Einstein, 69621 Villeurbanne cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.insa-lyon.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-301088" type="direct"/>
            <relation active="#struct-301232" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-301232" status="VALID">
          <idno type="IdRef">162105150</idno>
          <orgName>Institut National des Sciences Appliquées</orgName>
          <orgName type="acronym">INSA</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300284" status="VALID">
          <idno type="IdRef">028209966</idno>
          <idno type="ISNI">0000 0001 2158 1682</idno>
          <idno type="ROR">https://ror.org/04yznqr36</idno>
          <idno type="Wikidata">Q623154</idno>
          <orgName>Université Jean Monnet - Saint-Étienne</orgName>
          <orgName type="acronym">UJM</orgName>
          <date type="start">1969-03-27</date>
          <date type="end">2025-01-01</date>
          <desc>
            <address>
              <addrLine>10, Rue Tréfilerie – CS 8230142023 Saint-Étienne Cedex 2</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.univ-st-etienne.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-1327915" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-1327915" status="VALID">
          <idno type="IdRef">285395831</idno>
          <orgName>Université Jean Monnet (EPSCPE)</orgName>
          <orgName type="acronym">UJM EPE</orgName>
          <date type="start">2025-01-01</date>
          <desc>
            <address>
              <addrLine>10 rue Tréfilerie42100 Saint-Etienne</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.univ-st-etienne.fr/fr/index.html</ref>
          </desc>
        </org>
      </listOrg>
      <listOrg type="projects">
        <org type="anrProject" xml:id="projanr-41932" status="VALID">
          <idno type="anr">ANR-15-CE40-0012</idno>
          <orgName>GéoLie</orgName>
          <desc>Méthodes géométriques en théorie de Lie</desc>
          <date type="start">2015</date>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>