The Symbolic and cancellation-free formulae for Schur elements

Details The Symbolic and cancellation-free formulae for Schur elements The Symbolic and cancellation-free formulae for Schur elements

2011-10-27

arxiv.org/abs/1110.6069v1

Mathematics

Representation Theory

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Scientific paper

In this paper we give a symbolical formula and a cancellation-free formula for the Schur elements associated to the simple modules of the degenerate cyclotomic Hecke algebras. As some direct applications, we show that the Schur elements are symmetric with respect to the natural symmetric group action and are integral coefficients polynomials and we give a different proof of Ariki-Mathas-Rui's criterion on the semi-simplicity of degenerate cyclotomic Hecke algebras.

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