A cellular basis of the q-Brauer algebra related with Murphy bases of the Hecke algebras

2013/02/18 by Dung Tien Nguyen, Nguyen, Dung Tien
Mathematics · #16G30 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:16G30

paper · pdf · doi:10.48550/arxiv.1302.4272

21 pages

arxiv created 2013/09/13 · arxiv updated 2013/09/16

Abstract

A new basis of the q-Brauer algebra is introduced, which is a lift of Murphy bases of Hecke algebras of symmetric groups. This basis is a cellular basis in the sense of Graham and Lehrer. Subsequently, using combinatorial language we prove that the non-isomorphic simple q-Brauer modules are indexed by the e(q²)-restricted partitions of n-2k where k is an integer, 0 ≤ k ≤ [n/2]. When the q-Brauer algebra has low-dimension a criterion of semisimplicity is given, which is used to show that the q-Brauer algebra is in general not isomorphic to the BMW-algebra.

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