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A Frobenius formula for the characters of the Hecke algebras. (English) Zbl 0758.05099
In this paper, characters for representations of the Hecke algebra of type \(A_ n\) are studied. The natural action of this Hecke algebra on the tensor products of the standard representation of the quantum group \(U_ q(sl(n))\) is used. By rewriting this action in an appropriate form, a Frobenius type formula for the characters is deduced. Using this formula, a combinatorial rule is given to compute the irreducible characters of the Hecke algebra, and some tables are given. Connections with Hall-Littlewood symmetric functions and Kronecker products of symmetric groups are pointed out.

05E10 Combinatorial aspects of representation theory
20C15 Ordinary representations and characters
17B37 Quantum groups (quantized enveloping algebras) and related deformations
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