arXiv subjects
Publications and source records attributed to C. Dezelee.
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.
For a root system of type $B$ we study an algebra similar to a graded Hecke algebra, isomorphic to a subalgebra of the rational Cherednik algebra. We introduce principal series modules over it and prove an irreducibility criterion for these modules. We deduce similar results for an algebra associated to a root system of type $D$.
On donne une condition necessaire et suffisante pour l'existence de modules de dimension finie sur l'algebre de Cherednik rationnelle associee a un systeme de racines.