Discrete series characters and Fourier inversion on semisimple real Lie groups

D-modules and Characters of Semisimple Lie Groups

A famous theorem of Harish-Chandra asserts that all invariant eigendistributions on a semisimple Lie group are locally integrable functions. We show that this result and its extension to symmetric pairs are consequences of an algebraic property of a holonomic D-module defined by Hotta and Kashiwara.

Factorizations in the Irreducible Characters of Compact Semisimple Lie Groups

Our goal is to describe factorizations of the characters of irreducible representations of compact semisimple Lie groups. It is well-known that for a given Lie group G of rank n, the Virtual Representation Ring R(G) with the operations of tensor product, direct sum, and direct difference is isomorphic to a polynomial ring with integer coefficients and number of generators equal to n. As such, R...

Real-Variable Theory and Fourier Integral Operators on Semisimple Lie Groups and Symmetric Spaces of Real Rank One

Let G be a non-compact connected semisimple Lie group of real rank one with finite center, K a maximal compact subgroup of G and X = G/K an associated symmetric space of real rank one. We will prove that L(G) ∗ L(G) ⊆ L(G), which is a sharp endpoint estimate for the Kunze-Stein phenomenon. We will also show that the noncentered maximal operator M2f(z) = sup z∈B 1 |B| ∫ B f(z)dz is bounded from ...

Equivariant derived category and representation of real semisimple Lie groups

On Contractions of Semisimple Lie Groups

A limiting formula is given for the representation theory of the Cartan motion group associated to a Riemannian symmetric pair (G, K) in terms of the representation theory of G. Introduction. Let G be a connected Lie group with Lie algebra g, and H a closed subgroup with subalgebra b. The coset space G/H is called reductive [9, p. 389] if h admits an AdG(H) invariant complement m in g; i.e. a s...