Degree and valuation of the Schur elements of cyclotomic Hecke algebras

Abstract

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.

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