Mixed automorphic forms on 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...

Representations of Semisimple Lie Groups

Let G be a Lie group and § a Banach space. A representation n of G on § is a mapping which assigns to every element x in G a bounded linear operator n(x) on § such that the following two conditions are fulfilled: (1) 7t(xy) = n(x) 7i(y) (x, y e G),n(l) = / and (2) the mapping (x, tp) ->uz(x)y) of G x § into § is continuous. (Here 1 is the unit element of G and I is the unit operator,) In partic...

Integrable G-Strands on semisimple Lie groups

CNRS / Laboratoire de Météorologie Dynamique, École Normale Supérieure, Paris, France. Partially supported by a Projet Incitatif de Recherche contract from the Ecole Normale Supérieure de Paris. [email protected] Department of Mathematics, Imperial College London. London SW7 2AZ, UK. Partially supported by the European Research Council’s Advanced Grant 267382 FCCA. [email protected] Secti...

Representations of Semisimple Lie Groups

Fifty years ago, at the International Congress in Bologna, Hermann Weyl gave a report on representations of compact groups and, in particular, of compact Lie groups. Most of the important results had just been proved by him and by others, and at the time of his lecture, in 1928, the representation theory of compact Lie groups had become a very appealing subject. To a large extent, Weyl's theory...

Discontinuous Groups and Automorphic Forms