Computing cocharacters of sign trace identities in reduced notation

Author: Carini, Luisa

Source: Linear and Multilinear Algebra, Volume 54, Number 2, Number 2/March 2006 , pp. 147-156(10)

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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 where ? ? ? ? ? denotes the Kronecker product of the irreducible character of the symmetric group associated with the partition ? with itself and H(k,l;n) denotes the set of partitions of n ??=(? 1 = ? 2 = ···= ? n ) such that ? k+1 = l . In case of k ?=?2, l ?=?1, we 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, 7461–7478).

Keywords: Trace identities; Invariant theory; Kronecker product; Schur functions

Document Type: Research article

DOI: http://dx.doi.org/10.1080/03081080500286545

Affiliations: 1: Dipartimento di Matematica, Università di Messina, Salita Sperone 31, 98166, Messina, Italy

Publication date: 2006-03-01