Motive Representation Theory

Regents Of The University Of Michigan - Ann Arbor, Ann Arbor MI

Investigators

Abstract

A new type of integration, called motivic integration, has been proposed by M. Konsevitch and developed by Denef and Loeser. They show that many of the classical properties of p-adic integration can be extended to to the motivic context. The research of this proposal will adapt motivic integration to the representation theory and the harmonic analysis of reductive groups over fields of formal Laurent series in characteristic zero. This new theory will be developed from first principles, starting with the existence of motivic Haar measures. The starting point of much of modern mathematics is the theory of integration, as developed by Isaac Newton, and generations of mathematicians that have followed him. An unexpected development came in 1995, when the mathematician M. Kontsevich developed an entirely new way to integrate. This new tool will allow mathematicians to significantly enlarge the scope of mathematics. The research of this grant will accomplish part of this project, by using this new tool to enlarge the scope of representation theory, a branch of modern algebra.