COCHARACTERS OF POLYNOMIAL IDENTITIES OF UPPER TRIANGULAR MATRICES

Abstract

Let T(Uk) be the T-ideal of the polynomial identities of the algebra of k × k upper triangular matrices over a field of characteristic zero. We give an easy algorithm which calculates the generating function of the cocharacter sequence χn(Uk) = Σλ⊢n mλ(Uk)χλ of the T-ideal T(Uk). Applying this algorithm we have found the explicit form of the multiplicities mλ(Uk) in two cases: (i) for the "largest" partitions λ = (λ1,…,λn) which satisfy λk+1 +⋯+ λn = k - 1; (ii) for the first several k and any λ.