Cocharacters of polynomial identities of upper triangular matrices
  We give an easy algorithm which calculates the generating function of the cocharacter sequence of the T-ideal of the polynomial identities of the algebra of upper triangular matrices over a field of characteristic zero. Applying this algorithm we have found the explicit form of the multiplicities in two cases: (i) for the "largest" partitions; (ii) for matrices of small size and for all partitions. 
Silvia Boumova, Vesselin Drensky
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