DEMAZURE OPERATORS FOR COMPLEX REFLECTION GROUPS G(e,e,n)

Abstract

This paper is a continuation of the work in [RS], where we studied Demazure operators for the imprimitive complex reflection group W˜=G(e,1,n) and constructed a homogeneous basis of the coinvariant algebra SW˜. In this paper, we study a similar problem for the reflection subgroup W=G(e,e,n) of W˜. We prove, by assuming certain conjectures, that the operators Δw(w∈W) are linearly independent over the symmetric algebra S(V). We define a graded space HW in terms of Demazure operators, and we show that the coinvariant algebra SW is naturally isomorphic to HW. Then we can define a homogeneous basis of SW parametrized by w∈W.