[Mathkoll] MathKoll. am 24.03.04/Prof. Neretin

[Institut für Mathematik]

Mathematisches Kolloquium

EINLADUNG

zu einem

VORTRAG

von

Prof. Yurii Neretin
(Institut fuer Mathematik, Universitaet Wien)

mit dem Thema:

" Inverse limits of unitary groups, Hua densities, and infinite dimensional
analogs of Haar measure "

Abstract:
There exists a natural canonical  map from a unitary group $U(n+m)$ to
smaller unitary  group $U(n)$. It is given by an explicit formula $$
\begin{pmatrix}a&b\\c&d \end{pmatrix} \mapsto a-b(1+d)^{-1}c $$. The formula
arises to M.S. Livshits (=Livsic) works on spectral theory of
non-selfadjoint oprators in 1940-s.
We apply this map to evaluation of some matrix integrals of Hua Loo Keng
type and also construct a natural two-parametric family of measures on the
inverse limit of unitary groups. This inverse limit is not a group, but it
is a space with measure, where the infinite-dimensional unitary group acts
via left and right multiplications. We also give a non-formal introduction
to recent Borodin and Olshanski works on harmonic analysis on this inverse
limit.

Zeit: Mittwoch, 24. Maerz 2004
	15.45 Uhr (Kaffeejause), anschließend 16.15 Uhr Vortrag

Ort: Institut fuer Mathematik der Universitaet Wien, Nordbergstr. 15,
       Seminarraum C 2.09

Peter Michor
Harald Rindler