#
Branching problems for unitary representations

July 25 to July 29, 2011
at the

American Institute of Mathematics,
San Jose, California

organized by

Toshiyuki Kobayashi,
Bent Orsted,
and Birgit Speh

## Original Announcement

This workshop will focus on branching laws for the restriction of a unitary representation to a subgroup.
The central problem of the workshop
will be to find explicit branching laws. If the representations are discretely decomposable, then the
explicit branching laws are often of a combinatorial nature. Here
techniques from algebraic combinatorics will be extremely
important and many interesting combinatorial problems
should arise.

Another goal is elucidate the connection between the real and the *p*-adic situation.
and to analyze how different methods in the real and
*p*-adic case might lead to (conjecturally) similar phenomena. This
pertains in particular to the branching laws with discrete
spectrum.

## Material from the workshop

A list of participants.
The workshop schedule.

A report on the workshop activities.

Papers arising from the workshop:

Discrete branching laws for minimal holomorphic representations

by Jan Möllers and Yoshiki Oshima,

*J. Lie Theory 25 (2015), no. 4, 949-983 * MR3345043Duflo's conjecture for the branching to the Iwasawa AN-subgroup

by Gang Liu,

*Math. Ann. 362 (2015), no. 1-2, 107-120 * MR3343871The continuous spectrum in discrete series branching laws

by Benjamin Harris, Hongyu He, and Gestur Olafsson,

*Internat. J. Math. 24 (2013), no. 7, 1350049, 29 pp * MR3084730Discrete components in restriction of unitary representations of rank one semisimple Lie groups

by Genkai Zhang,

*J. Funct. Anal. 269 (2015), no. 12, 3689-3713 * MR3418069