Generalized graded Hecke algebra for complex reflection group of type G(r,1,n)

Abstract

We study the representation theory of a generalized graded Hecke algebra associated to a complex reflection group of type G(r,1,n), defined by Ram and Shepler. We use a realization of this algebra in the corresponding symplectic reflection algebra to prove a PBW theorem. We define principal series modules and prove an irreducibility criterion for them.

12 pages

Cited by in corpus (1)

• Jack polynomials and the coinvariant ring of $G(r,p,n)$