Asymptotics of representations
Click on picture to find out it's significance.
Note: Numbered references refer to my vita.
Associated to any nice representation will
be a family of matrix coefficient functions. Harish-Chandra pioneered the
idea of studying the asymptotic expansions of the matrix coefficients to
gain insight into the representation theory of the Lie group. Beginning
with my thesis [1], I have undertaken a program to analyze
these expansions through a functorial link to a category of highest
weight representations. This uses the theory of Jacquet modules
and my work with Luis Casian
in [12-14] was a big step forward in understanding
these modules and expansions. The techniques involved are geometric and
algebraic, using the theory of D-modules, intersection cohomology and
various cohomological techniques.