Small Representations of Finite Groups

Abstract

Finite group theorists have established many formulas that express interesting properties of a finite group in terms of sums of characters of the group. An obstacle to applying these formulas is lack of control over the dimensions of representations of the group. In particular, the representations of small dimension tend to contribute the largest terms to these sums, so a systematic knowledge of these small representations could lead to proofs of some of these facts. Despite the classification of Lusztig of irreducible representations for finite groups of Lie type, this aspect remains obscure. This talk will discuss a conjectural method for constructing the small representations of finite classical groups.

The method is closely related to the theory of theta series, and has an analog over local fields.

About the speaker

Prof. Roger Howe received his PhD from UC Berkeley in 1969, and has been a faculty member of Yale University since 1974. He was appointed William R. Kenan Jr. Professor of Mathematics in 2002. His mathematical research investigates symmetry and its applications. He is well-known for his contributions to representation theory, and in particular for the notion of a reductive dual pair, sometimes known as a Howe pair. He is a Fellow of the American Academy of Arts and Sciences and a Member of the US National Academy of Sciences.