Y-proper graded cocharacters of upper-triangular matrices od order m graded by the m-tuple ϕ=(0,0,1,...,m-2)

Abstract

Let F be a field of characteristic 0. We consider the algebra U Tm(F ) of upper-triangular matrices of order m endowed with an elementary Zm-grading induced by the m-tuple φ = (0, 0, 1, . . . , m − 2), then we compute its Y -proper graded cocharacter sequence and we give the explicit formulas for the multiplicities in the case m = 2, 3, 4, 5.