
SIGMA 4 (2008), 017, 19 pages arXiv:0802.0974
https://doi.org/10.3842/SIGMA.2008.017
Contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson
Branching Laws for Some Unitary Representations of SL(4,R)
Bent Ørsted ^{a} and Birgit Speh ^{b}
^{a)} Department of Mathematics, University of Aarhus, Aarhus, Denmark
^{b)} Department of Mathematics, 310 Malott Hall, Cornell University, Ithaca, NY 148534201, USA
Received September 10, 2007, in final form January
27, 2008; Published online February 07, 2008
Abstract
In this paper we consider the restriction of a unitary
irreducible representation of type A_{q}(λ) of
GL(4,R) to reductive subgroups H which are the fixpoint sets
of an involution. We obtain a formula for the restriction to the
symplectic group and to GL(2,C), and as an application we
construct in the last section some representations in the cuspidal
spectrum of the symplectic and the complex general linear group.
In addition to working directly with the cohmologically induced
module to obtain the branching law, we also introduce the
useful concept of pseudo dual pairs of subgroups in a reductive
Lie group.
Key words:
semisimple Lie groups; unitary representation; branching laws.
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