Groups and Dynamics Seminar

Date: February 8, 2017

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Roger Howe

Title: Unitary representations of discrete nilpotent groups, and C^* algebras

Abstract: This talk will review the theory of unitary representations of finitely generated, torsion-free nilpotent groups (aka, discrete subgroups of simply connected nilpotent Lie groups). The finite dimensional irreducible representations can (almost) be described by an analog of Kirillov's orbit method, which will also be reviewed. The infinite dimensional irreducible unitary representations are too disorderly to classify in a simple way, as will be shown by example. However, there is a reasonable way, based on C^* algebras, to collect the irreducible representations into chunks, which can then be classified in analogy with the finite-dimensional representations.