In ( Regev,A., 1987, Sign trace identities, Linear and Multilinear Algebra, 21,1-28),Regev applied the representation theory of a general Lie superalgebra to generalize the theory of trace identities as developed by Procesi and Razmyslov. Regev showed that certain cocharacters arising from sign trace identities were given by the sum of the Kronecker product of the irreducible character of the symmetric group indexed by a certain partition of n with itself. In this paper we show how to compute some multiplicities which occur in the expansion of the cocharacter in terms of irreducible characters by using the reduced notation ( Scharf,T., Thibon, J.-Y. and Wybourne B. , 1993, Reduced notation, inner plethysms and the symmetric group. Journal of Physics A: Mathematical and General, 26, 7461-7468).
Computing cocharacters of sign trace identities in reduced notation
CARINI, Luisa
2006-01-01
Abstract
In ( Regev,A., 1987, Sign trace identities, Linear and Multilinear Algebra, 21,1-28),Regev applied the representation theory of a general Lie superalgebra to generalize the theory of trace identities as developed by Procesi and Razmyslov. Regev showed that certain cocharacters arising from sign trace identities were given by the sum of the Kronecker product of the irreducible character of the symmetric group indexed by a certain partition of n with itself. In this paper we show how to compute some multiplicities which occur in the expansion of the cocharacter in terms of irreducible characters by using the reduced notation ( Scharf,T., Thibon, J.-Y. and Wybourne B. , 1993, Reduced notation, inner plethysms and the symmetric group. Journal of Physics A: Mathematical and General, 26, 7461-7468).Pubblicazioni consigliate
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