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Article Dans Une Revue Journal of Physics A: Mathematical and Theoretical Année : 2009

Braids, Shuffles and Symmetrizers

Résumé

Multiplicative analogues of the shuffle elements of the braid group rings are introduced; in local representations they give rise to certain graded associative algebras (b-shuffle algebras). For the Hecke and BMW algebras, the (anti)-symmetrizers have simple expressions in terms of the multiplicative shuffles. The (anti)-symmetrizers can be expressed in terms of the highest multiplicative 1-shuffles (for the Hecke and BMW algebras) and in terms of the highest additive 1-shuffles (for the Hecke algebras). The spectra and multiplicities of eigenvalues of the operators of the multiplication by the multiplicative and additive 1-shuffles are examined.

Dates et versions

hal-00473349 , version 1 (15-04-2010)

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Citer

A. P. Isaev, O. V. Ogievetsky. Braids, Shuffles and Symmetrizers. Journal of Physics A: Mathematical and Theoretical, 2009, 42 (30), pp.304017. ⟨10.1088/1751-8113/42/30/304017⟩. ⟨hal-00473349⟩
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