The alternating presentation of $U_q(\widehat{gl_2})$ from Freidel-Maillet algebras - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Nuclear Physics B Année : 2021

The alternating presentation of $U_q(\widehat{gl_2})$ from Freidel-Maillet algebras

Pascal Baseilhac

Résumé

An infinite dimensional algebra denoted $\bar{\cal A}_q$ that is isomorphic to a central extension of $U_q^+$ - the positive part of $U_q(\widehat{sl_2})$ - has been recently proposed by Paul Terwilliger. It provides an `alternating' Poincar\'e-Birkhoff-Witt (PBW) basis besides the known Damiani's PBW basis built from positive root vectors. In this paper, a presentation of $\bar{\cal A}_q$ in terms of a Freidel-Maillet algebra is obtained. Using this presentation: (a) finite dimensional tensor product representations for $\bar{\cal A}_q$ are constructed; (b) explicit isomorphisms from $\bar{\cal A}_q$ to certain Drinfeld type `alternating' subalgebras of $U_q(\widehat{gl_2})$ are obtained; (c) the image in $U_q^+$ of all the generators of $\bar{\cal A}_q$ in terms of Damiani's root vectors is obtained. A new tensor product decomposition of $U_q(\widehat{sl_2})$ in terms of Drinfeld type `alternating' subalgebras follows. The specialization $q\rightarrow 1$ of $\bar{\cal A}_q$ is also introduced and studied in details. In this case, a presentation is given as a non-standard Yang-Baxter algebra. This paper is dedicated to Paul Terwilliger for his 65th birthday.
Fichier principal
Vignette du fichier
S0550321321000973.pdf (1.01 Mo) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03008860 , version 1 (24-04-2023)

Licence

Identifiants

Citer

Pascal Baseilhac. The alternating presentation of $U_q(\widehat{gl_2})$ from Freidel-Maillet algebras. Nuclear Physics B, 2021, 967 (June 2021), pp.115400. ⟨10.1016/j.nuclphysb.2021.115400⟩. ⟨hal-03008860⟩
69 Consultations
15 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More