# Symplectic Mackey Theory

## GAP Seminar

## Meeting Details

For more information about this meeting, contact Mathieu Stienon, Ping Xu, Nigel Higson.

**Speaker:** Francois Ziegler, Georgia Southern University

**Abstract:** When a Lie group G has a closed normal subgroup N, the â€œMackey Machineâ€ breaks down the classification of its irreducible representations into two smaller problems:
a) find the irreducible representations of N;
b) find the irreducible projective representations of certain subgroups of G/N.
The desired classification often follows inductively.
Key parts of this machine are
1) the â€œinducing constructionâ€ (building representations of G out of those of its subgroups);
2) the â€œimprimitivity theoremâ€ (characterizing the range of the inducing construction);
3) a â€œtensoringâ€ construction (combining objects of types a) and b) above).
Many years ago Kazhdan, Kostant and Sternberg defined the notion of inducing a hamiltonian action from a Lie subgroup, thus introducing a purely symplectic geometrical analog of 1); and the question arose whether analogs of 2) and 3) could be found and built into an effective â€œsymplectic Mackey Machineâ€. In this talk I will describe a complete solution to this problem, obtained recently.

## Room Reservation Information

**Room Number:** 106 McAllister

**Date:** 03/17/2015

**Time:** 2:30pm - 3:30pm