Degree and valuation of the Schur elements of cyclotomic Hecke algebras

Details Degree and valuation of the Schur elements of cyclotomic Hecke algebras Degree and valuation of the Schur elements of cyclotomic Hecke algebras

2008-02-28

arxiv.org/abs/0802.4306v2

J. Algebra 320 (2008), 3935-3949

Mathematics

Representation Theory

19 pages, the paper has been reorganized and shortened considerably without changes to the mathematical content, the introduct

Scientific paper

10.1016/j.jalgebra.2008.07.024

Following the generalization of the notion of families of characters, defined by Lusztig for Weyl groups, to the case of complex reflection groups, thanks to the definition given by Rouquier, we show that the degree and the valuation of the Schur elements (functions A and a) remain constant on the "families" of the cyclotomic Hecke algebras of the exceptional complex reflection groups. The same result has already been obtained for the groups of the infinite series and for some special cases of exceptional groups.

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