Representations and Types of p-adic Groups

Purdue University, West Lafayette IN

Investigators

Abstract

Recent work of the PI and J. Kim provides enough types to classify all representations of many p-adic reductive groups. It remains to clarify what parametrizes those types. Moreover, the PI would like to understand how types are related to Langlands parameters. In addition, the project seek to study a problem related to Bruhat decomposition which arises in the theory of partial Bessel functions and local coefficients. These problems are all part of the Langlands program, one of the most influence programme in mathematics linking number theory and analysis. The representation theory problems here deal with some of the local analysis in the program, and have deep connections with arithmetic and geometry.