ON SOME REPRESENTATIONS OF DEGENERATE AFFINE HECKE ALGEBRAS OF TYPE BCn

The degenerate affine Hecke algebra (dAHA) of any finite Coxeter group was defined by Drinfeld and Lusztig([Dri],[Lus]). It is generated by the group algebra of the Coxeter group and by the commuting generators yi with some relations. In [AS], the authors give a Lie-theoretic construction of representations of the dAHA of type An−1. They construct a functor from the BGG category of slN to the category of finite dimensional representations of the dAHA of type An−1. They also describe the image of some modules, e.g. the Verma modules, under this functor. In [CEE], this construction is generalized from the BGG category to the category of slN -bimodules and is upgraded to a Lie-theoretic construction of representations of degenerate double affine Hecke algebra (dDAHA) of type An−1. In [EFM], the authors generalize the Lie-theoretic constructions in [AS] and [CEE] to the type BCn root system. They construct a functor: