Y-proper graded cocharacters of upper-triangular matrices od 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 UT_m(F) of upper triangular matrices of order m endowed with na elementar 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=2,3,4,5. 
Lucio Centrone and Alessio Cirrito
math.RA