Cocharacters of polynomial identities of block triangular matrices

2011/12/04 by Vesselin Drensky, Drensky, Vesselin, Boyan Kostadinov +1
Mathematics · #05A15 #05E05 #05E10 #16R10 #20C30 #Combinatorics (math.CO) #FOS: Mathematics #Rings and Algebras (math.RA) #math.CO #math.RA #msc:05A15 #msc:05E05 #msc:05E10 #msc:16R10 #msc:20C30

paper · pdf · doi:10.48550/arxiv.1112.0792

Slightly updated version of the preprint in 2011

arxiv created 2016/01/12 · arxiv updated 2016/01/13

Abstract

We give an algorithm which calculates the generating function of the cocharacter sequence of the polynomial identities of the algebra of upper block triangular (p+2q) x (p+2q) matrices over a field of characteristic zero with diagonal consisting of p copies of 1 x 1 and q copies of 2 x 2 matrices. We have found the explicit form of the multiplicities and their asymptotic behaviour for small values of p and q.

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