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**Harvard**

Zhang, G. (2010) *Degenerate principal series representations and their holomorphic extensions*.

** BibTeX **

@article{

Zhang2010,

author={Zhang, Genkai},

title={Degenerate principal series representations and their holomorphic extensions},

journal={Advances in Mathematics},

issn={0001-8708},

volume={223},

issue={5},

pages={1495-1520},

abstract={Let X=H/L be an irreducible real bounded symmetric domain realized as a real form in an Hermitian symmetric domain D=G/K. The intersection S of the Shilov boundary of D with X defines a distinguished subset of the topological boundary of X and is invariant under H. It can be realized as S=H/P for certain parabolic subgroup P of H. We study the spherical representations of H induced from P. We find formulas for the spherical functions in terms of the Macdonald hypergeometric function. This generalizes the earlier result of Faraut–Koranyi for Hermitian symmetric spaces D. We consider a class of H-invariant integral intertwining operators from the representations on L2(S) to the holomorphic representations of G restricted to H. We construct a new class of complementary series for the groups H=SO(n,m), SU(n,m) (with n−m>2) and Sp(n,m) (with n−m>1). We realize them as discrete components in the branching rule of the analytic continuation of the holomorphic discrete series of G=SU(n,m), SU(n,m)×SU(n,m) and SU(2n,2m) respectively.},

year={2010},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 114062

A1 Zhang, Genkai

T1 Degenerate principal series representations and their holomorphic extensions

YR 2010

JF Advances in Mathematics

SN 0001-8708

VO 223

IS 5

SP 1495

OP 1520

AB Let X=H/L be an irreducible real bounded symmetric domain realized as a real form in an Hermitian symmetric domain D=G/K. The intersection S of the Shilov boundary of D with X defines a distinguished subset of the topological boundary of X and is invariant under H. It can be realized as S=H/P for certain parabolic subgroup P of H. We study the spherical representations of H induced from P. We find formulas for the spherical functions in terms of the Macdonald hypergeometric function. This generalizes the earlier result of Faraut–Koranyi for Hermitian symmetric spaces D. We consider a class of H-invariant integral intertwining operators from the representations on L2(S) to the holomorphic representations of G restricted to H. We construct a new class of complementary series for the groups H=SO(n,m), SU(n,m) (with n−m>2) and Sp(n,m) (with n−m>1). We realize them as discrete components in the branching rule of the analytic continuation of the holomorphic discrete series of G=SU(n,m), SU(n,m)×SU(n,m) and SU(2n,2m) respectively.

LA eng

DO 10.1016/j.aim.2009.09.014

LK http://dx.doi.org/10.1016/j.aim.2009.09.014

OL 30