Abstract: In this talk I hope to give an overview of the subject considered in my PhD thesis, which I will defend on December 21st. It concerns the representation theory of Lie groups.
A representation of a Lie group is an action of the group on a (possibly infinite dimensional) vector space. When the group under consideration is non-compact these representations often appear in `analytic families': families of representations of the same group on the same vector space but with actions that vary holomorphically as a function of some complex parameter. (We will illustrate this in the Fourier theory on R^n.) My research tries to understand this parameter dependence and to answer for families as a whole some of the questions classically asked for individual representations - notably about irreducibility and the relation between `infinitesimal' and `global' behavior. All results are joint work with Erik van den Ban.
It seems impossible to give a talk like this without introducing a lot of definitions but in order to appeal to a broad mathematical audience I will try to convey along with the mathematical concepts some feeling of who are the good, the bad and the ugly.
Here is a link to the slides of Vincent’s talk.
Location: room 611 of the Wiskunde building (campus De Uithof) Budapestlaan 6, Utrecht.
Date and time: Thursday, December 10, 2009 15:30-16:30. The lecture is preceded by coffee, tea, and cookies from 15.00 to 15.30 hour in the same room.
Schedule of the Utrecht math colloquium : Next term’s talks, This year's talks. Last year's talks. Guidelines for speakers.
Other math colloquia : TU Delft, Leiden, UvA Amsterdam, VU Amsterdam, Nijmegen.
Organisers : Gil Cavalcanti, Wilberd van der Kallen and Paul Zegeling