Spherical birational sheets in reductive groups

Spherical D - modules and Representations of Reductive Lie Groups

We study the representations of reductive Lie groups which occur in the space of smooth functions on indefinite symmetric spaces. We characterize these representations in the theory of Dmodules by a condition on the support and a condition on the fibers. This enables us to simplify Oshima-Matsuki's theorem on the discrete series of indefinite symmetric spaces, and to prove an L2-multiplicity on...

GENERALIZED SPHERICAL FUNCTIONS ON REDUCTIVE p-ADIC GROUPS

Let G be the group of rational points of a connected reductive p-adic group and let K be a maximal compact subgroup satisfying conditions of Theorem 5 from Harish-Chandra (1970). Generalized spherical functions on G are eigenfunctions for the action of the Bernstein center, which satisfy a transformation property for the action of K. In this paper we show that spaces of generalized spherical fu...

Reductive Groups

Conjugacy in Reductive Groups

Let G be a reductive algebraic group and H be a connected semisimple subgroup of G. The dimension data consists of the collection { dimV H } with V H denoting the space of points in V fixed by H , and where (ρ, V ) runs through all representations of G. One may ask if the dimension data determine H up to conjugacy or at least isomorphism. In other words, If H and H ′ have the same dimension dat...

Representations of Reductive Groups

This course consists of two parts. In the first we will study representations of reductive groups over local non-archimedian fields [ such as Qp and Fq((s))]. In this part I’ll closely follow the notes of the course of J.Bernstein. Moreover I’ll often copy big chanks from these notes. In the second the representations of reductive groups over 2-dimensional local fields [ such as Qp((s))]. In th...