COCHARACTERS OF POLYNOMIAL IDENTITIES OF UPPER TRIANGULAR MATRICES

Abstract

Let T(U k ) 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 χ n (U k ) = Σ λ⊢n m λ (U k )χ λ of the T-ideal T(U k ). Applying this algorithm we have found the explicit form of the multiplicities m λ (U k ) in two cases: (i) for the "largest" partitions λ = (λ 1 ,…,λ n ) which satisfy λ k+1 +⋯+ λ n = k - 1; (ii) for the first several k and any λ.