Cocharacters of polynomial identities of block triangular matrices

TL;DR

This paper presents an algorithm to compute the generating function of cocharacter sequences for polynomial identities of upper block triangular matrices, providing explicit multiplicities and asymptotic behavior for small parameters.

Contribution

It introduces a novel algorithm for calculating the generating function of cocharacter sequences in polynomial identities of block triangular matrices, with explicit formulas and asymptotic analysis.

Findings

Explicit form of multiplicities for small p and q

Asymptotic behavior of multiplicities analyzed

Algorithm for generating function calculation provided

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.