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Let F be a field of characteristic 0. We consider the algebra UT_m(F) ofupper triangular matrices of order m endowed with na elementar Z_m-gradinginduced by the m-tuple phi=(0,0,1,...,m-2), then we compute its Y-proper gradedcocharacter sequence and we give the explicit formulas for the multiplicitiesin the case m=2,3,4,5.

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