Tel Aviv University.
Sackler Distinguished Lecture
SPEAKER: Toshiyuki Kobayashi, University of Tokyo
TITLE: Branching Problems of Unitary Representations
DATE: Monday, 7 May, 2007
PLACE: Screiber building room 006, TAU
TIME: 12:15
For further information please contact:
Joseph Bernstein
Phone: 054-4720559
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ABSTRACT:
Branching problems ask how an irreducible representation of a
group decomposes when restricted to a subgroup.
In these Lectures, I plan to give a survey on new aspects on branching
problems of unitary representations of reductive Lie groups. The first
half will be based on representation theoretic viewpoints. Following an
observation of wild feature of branching problems with respect to
non-compact subgroups in a general setting, I will introduce the notion
of admissible restrictions as a nice framework that enjoys two
properties: finiteness of multiplicities and discreteness of spectrum. A
criterion for finite multiplicity and discretely decomposable
restrictions will be presented. The idea of our proof stems from
microlocal analysis and algebraic geometry. Furthermore, an exclusive
law of discrete spectrum is formalized for inductions and restrictions.
The second half deals with applications. Admissible restrictions may
give tools for the study of representations for bigger groups via
restrictions, and for the construction of irreducibles of smaller groups
via branching laws. Once we know that restrictions are discretely
decomposable, we may employ an algebraic approach to branching problems.
In this direction, new branching formulas have been recently obtained in
various settings, of which I plan to illustrate by examples. Finally, I
will discuss some applications of discretely decomposable branching laws
to other areas of mathematics. The topics include (1) topological
properties of modular varieties in locally symmetric spaces, (2) a
construction of new discrete series representations for non-Riemannian
non-symmetric homogeneous spaces. If time allows, I may mention also a
mystery between tessellation of (and discontinuous groups for)
non-Riemannian homogeneous spaces and branching problems of unitary
representations
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Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel
Announcement from: Joseph Bernstein