Jucys-Murphy elements for Birman-Murakami-Wenzl algebras

2009/12/20 by A. P. Isaev, Isaev, A. P., O. V. Ogievetsky +1 · 1 citation
Mathematics · #20C08 #81R50 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #msc:20C08 #msc:81R50

paper · pdf · doi:10.48550/arxiv.0912.4010

Proceedings of International Workshop "Supersymmetries and Quantum Symmetries", Dubna, 2009

arxiv created 2009/12/20 · arxiv updated 2010/01/14

Abstract

The Birman-Wenzl-Murakami algebra, considered as the quotient of the braid group algebra, possesses the commutative set of Jucys--Murphy elements. We show that the set of Jucys--Murphy elements is maximal commutative for the generic Birman-Wenzl-Murakami algebra and reconstruct the representation theory of the tower of Birman-Wenzl-Murakami algebras.

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