Seminar for Unitary Representations and Automorphic Forms

On Wednesday, June 18, 2025, 17:15 hours, Gordan Savin (University of Utah) will hold lecture in lecture room 109 titled:

Finiteness of big theta for (exceptional) real groups. 

Abstract: In order to obtain a correspondence between representations of two Lie algebras, one needs a vector space with an action of the two Lie algebras.

Then, for each irreducible representation of one Lie algebra, one can define the full lift (also called big-theta). It is a representation of the other Lie algebra. 

Of interest to us are situations when the big theta has finite length with unique quotient. The we have a correspondence of representations of two algebras. 

 Working in this general setting I will explain a strategy to prove that big theta has finite length. 

For certain (quaternionic) exceptional dual pairs this takes us to a problem with quaternionic representations, introduced by Gross and 

Wallach. I will explain what these are, and then how to establish the desired properties. 

This is a joint work with Bakic and Loke.