Branching laws for some unitary representations of SL(4,R)

TY - JOUR

T1 - Branching laws for some unitary representations of SL(4,R)

AU - Ørsted, Bent

AU - Speh, Birgit

N1 - Paper id:: 017

PY - 2008

Y1 - 2008

N2 - In this paper we consider the restriction of a unitary irreducible representation of type Aq(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.

AB - In this paper we consider the restriction of a unitary irreducible representation of type Aq(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.

U2 - 10.3842/SIGMA.2008.017

DO - 10.3842/SIGMA.2008.017

M3 - Journal article

SN - 1815-0659

VL - 4

JO - Symmetry, Integrability and Geometry: Methods and Applications

JF - Symmetry, Integrability and Geometry: Methods and Applications

ER -