Constructing automorphic representations in split classical groups

The Problem of Classifying Automorphic Representations of Classical Groups

In this article we shall give an elementary introduction to an important problem in representation theory. The problem is to relate the automorphic representations of classical groups to those of the general linear group. Thanks to the work of a number of people over the past twenty-five years, the automorphic representation theory of GL(n) is in pretty good shape. The theory for GL(n) now incl...

Automorphic Representations of Adele Groups

Classical automorphic forms and representations of SL ( 2 )

This essay will explain the relationship between classical automorphic forms and representations of GL 2 (R). The classical theory of automorphic forms, in spite of initial appearances, is about the group GL 2 , not SL 2. The classical theory is concerned with functions on the upper half plane, which is acted on by fractional linear transformations in GL pos 2 (R), and it happens that the inter...

Spherical unitary representations for split groups

1. Basic examples.

Constructing maximal subgroups of classical groups

In this paper we show how to construct the maximal subgroups of the finite classical groups of linear, symplectic or unitary type in low-degree