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.
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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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Communicated by J. S. Wilson.
This research was supported by NSFC grant no. 11101037.
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Zhao, D. The symbolical and cancellation-free formulae for Schur elements. Monatsh Math 173, 441–453 (2014). https://doi.org/10.1007/s00605-013-0500-7
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DOI: https://doi.org/10.1007/s00605-013-0500-7