Monatshefte für Mathematik

, Volume 173, Issue 3, pp 441–453 | Cite as

The symbolical and cancellation-free formulae for Schur elements

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Abstract

In this paper we give the symbolical formula and cancellation-free formula for the Schur elements associated to the simple modules of the degenerate cyclotomic Hecke algebras. As some applications, we show that the Schur elements are symmetric polynomials with rational integer coefficients and give a different proof of Ariki–Mathas–Rui’s criterion on the semisimplicity of the degenerate cyclotomic Hecke algebras.

Keywords

(Degenerate) cyclotomic Hecke algebras Complex reflection groups Schur elements \(L\)-symbols 

Mathematics Subject Classification (2010)

Primary 16G99 Secondary 20C20 20G05 
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Notes

Acknowledgments

This work was partially carried out while the author was visiting the Academy of Mathematics and Systems Science, CAS in Beijing. We are most deeply indebted to Nanhua Xi and Yang Han for their invaluable help. We are grateful to Ming Fang for useful conversations.

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Copyright information

© Springer-Verlag Wien 2013

Authors and Affiliations

  1. 1.School of Applied MathematicsBeijing Normal University at ZhuhaiZhuhaiChina

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