Abstract We construct a family of representations affine Hecke algebras, which depend on number auxiliary parameters $$g_i$$ g i , and we refer to as metaplectic representations. realize these quotients certain parabolically induced modules, apply the method Baxterizati...

In this paper we classify and give Kazhdan-Lusztig type character formulas for equivariantly irreducible representations of Lie algebras reductive algebraic groups over a field large positive characteristic. The equivariance is with respect to group whose connected component torus. Character computation done in two steps. First, treat the case distinguished <inline-formula content-type="math/ma...

We study a problem concerning parabolic induction in certain p-adic unitary groups. More precisely, for $E/F$ quadratic extension of fields the associated group $G=\mathrm{U}(n,n)$ contains subgroup $P$ with Levi component $L$ isomorphic to $\mathrm{GL}_n(E)$. Let $\pi$ be an irreducible supercuspidal representation depth zero. use Hecke algebra methods determine when parabolically induced $\io...

For any reductive Lie algebra g and commutative, associative, unital algebra S, we give a complete classification of the simple weight modules of g ⊗ S with finite weight multiplicities. In particular, any such module is parabolically induced from a simple admissible module for a Levi subalgebra. Conversely, all modules obtained in this way have finite weight multiplicities. These modules are i...

The action of a reductive algebraic group G on G/P−, where P− is a parabolic subgroup, differentiates to a representation of the Lie algebra g of G by vector fields on U+, the unipotent radical of a parabolic opposite to P−. We show that both the regular functions on U+ and the polynomial vector fields on U+ form g-modules that are dual to parabolically induced modules, construct an explicit co...

We continue our study of the tempered spectrum of quasi-split classical groups. Here we examine the case of the special orthogonal groups of odd dimension. While this is the last of the classical groups to be examined, it is the first for which our results address the tempered spectrum whose supercuspidal support is an arbitrary maximal parabolic subgroup, as we describe below. We continue to s...

This paper is concerned with representations of split orthogonal and quasi-split unitary groups over a nonarchimedean local field which are not generic, but which support a unique model of a different kind, the generalized Bessel model. The properties of the Bessel models under induction are studied, and an analogue of Rodier’s theorem concerning the induction of Whittaker models is proved for ...