Click here for a pdf version of my research statement.

Next: Bessel Models for General Up: Research Statement Previous: Research Statement

Introduction

Section 2 contains the main result of my thesis. Here a multiplicity one theorem for the space of Bessel Models of a General Induced Representation is given. This generalizes a result of Wallach given in [W,86], and was motivated by a question asked by Dipendra Prasad during his visit to UCSD in 2007-2008 [P-TB]. In my joint work with Wallach we answer his question in the affirmative [G-W]. In [G-1] I prove a similar result in a more general setting.

In section 3 I describe an application of this result that I had in mind when I started working on my thesis. The idea of this section is to use Howe's theory of dual pairs to describe the space using the representation theory of the group , with . This description is a generalization of a result of Howe when , and is motivated by the idea of Venkatesh and Sakellaridis [S-V] of relating the harmonic analysis on a spherical variety with the representation theory of another group. What this example shows is that this idea may be useful not only for spherical varieties, but for a larger class of homogeneous spaces. At the end of this section I state a conjecture that relates this example with the results given in section 2.

In the last section I discuss the current state of the conjecture mentioned in the above paragraph and a plan for its proof. In this section I also describe possible extensions of the results given here, and my plans for future research.