The Symbolic and cancellation-free formulae for Schur elements

Abstract

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.

To appear in Monatshefte fur Mathematik

References in corpus (3)

• Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
• Schur elements for the Ariki-Koike algebra and applications
• The degenerate analogue of Ariki's categorification theorem