Department of Mathematics

Indian Institute of Science

Bangalore 560 012

 

SEMINAR

 

Speaker

:

 Prof. Gerald B. Folland
Affiliation : University of Washington

Subject Area

:

Mathematics

 

Venue

:

Lecture Hall I, Department of Mathematics

 

Time

:

4.00-5.00 p.m.

 

Date  

:

January30, 2012 (Monday)

Title

:

"Some representations of the discrete Heisenberg group"
Abstract

:

The operators $f(t) \rightarrow f(t-a)$ and $f(t) \rightarrow e^{2\pi bt} f(t)$ on $L^2(\mathbb R)$ generate unitary representations of the discrete Heisenberg group $H$ with central character $e^{2\pi abz}$. What are the irreducible representations of $H$ with this central character, and how can one synthesize the representation just described from them ? When $ab$ is rational, the answers are quite straight forward, but when $ab$ is irrational things are much more complicated. We shall describe results in both cases.