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

Let F be a field of characteristic 0. We consider the algebra UTm(F) of upper triangular matrices of order m endowed with an elementary Z(m)-grading induced by the m-tuple phi = (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 = 2,3,4,5425546562FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESP2013/06752-