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SIGMA, 2008, Volume 4, 017, 19 pages (Mi sigma270)  

This article is cited in 10 scientific papers (total in 10 papers)

Branching Laws for Some Unitary Representations of $\mathrm{SL}(4,\mathbb R)$

Bent Ørsteda, Birgit Spehb

a Department of Mathematics, University of Aarhus, Aarhus, Denmark
b Department of Mathematics, 310 Malott Hall, Cornell University, Ithaca, NY 14853-4201, USA

Abstract: In this paper we consider the restriction of a unitary irreducible representation of type $A_{\mathfrak q}(\lambda)$ of $GL(4,\mathbb R)$ 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 $GL(2,\mathbb C)$, 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.

Keywords: semisimple Lie groups; unitary representation; branching laws

DOI: https://doi.org/10.3842/SIGMA.2008.017

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Full text: http://emis.mi.ras.ru/.../017
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Bibliographic databases:

ArXiv: 0802.0974
MSC: 22E47; 11F70
Received: September 10, 2007; in final form January 27, 2008; Published online February 7, 2008
Language:

Citation: Bent Ørsted, Birgit Speh, “Branching Laws for Some Unitary Representations of $\mathrm{SL}(4,\mathbb R)$”, SIGMA, 4 (2008), 017, 19 pp.

Citation in format AMSBIB
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\by Bent {\O}rsted, Birgit Speh
\paper Branching Laws for Some Unitary Representations of $\mathrm{SL}(4,\mathbb R)$
\jour SIGMA
\yr 2008
\vol 4
\papernumber 017
\totalpages 19
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\crossref{https://doi.org/10.3842/SIGMA.2008.017}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Pevzner M., “Covariant quantization: spectral analysis versus deformation theory”, Japanese Journal of Mathematics, 3:2 (2008), 247–290  crossref  mathscinet  zmath  isi  scopus
    2. T. Kobayashi, “Hidden Symmetries and Spectrum of the Laplacian on an Indefinite Riemannian Manifold”, Contemporary Mathematics, 484 (2009), 73–87  crossref  mathscinet  zmath  isi
    3. Sekiguchi H., “Branching rules of Dolbeault cohomology groups over indefinite Grassmannian manifolds”, Proc Japan Acad Ser A Math Sci, 87:3 (2011), 31–34  crossref  mathscinet  zmath  isi  scopus
    4. Speh B., “Restriction of Some Representations of U(P,Q) to a Symmetric Subgroup”, Representation Theory and Mathematical Physics, Contemporary Mathematics, 557, eds. Adams J., Lian B., Sahi S., Amer Mathematical Soc, 2011, 371–388  crossref  mathscinet  zmath  isi
    5. Kobayashi T., “Branching Problems of Zuckerman Derived Functor Modules”, Representation Theory and Mathematical Physics, Contemporary Mathematics, 557, eds. Adams J., Lian B., Sahi S., Amer Mathematical Soc, 2011, 23–40  crossref  mathscinet  zmath  isi
    6. Harris, B; He, HY; Olafsson, G, “The continuous spectrum in discrete series branching laws”, International Journal of Mathematics, 24:7 (2013), 1350049  crossref  mathscinet  zmath  isi  scopus
    7. Gourevitch D., Sahi S., Sayag E., “Invariant Functionals on Speh Representations”, Transform. Groups, 20:4 (2015), 1023–1042  crossref  mathscinet  zmath  isi  scopus
    8. Oshima Y., “on the Restriction of Zuckerman'S Derived Functor Modules a(Q)(Lambda) To Reductive Subgroups”, Am. J. Math., 137:4 (2015), 1099–1138  crossref  mathscinet  zmath  isi  scopus
    9. Vargas J.A., “Associated symmetric pair and multiplicities of admissible restriction of discrete series”, Int. J. Math., 27:12 (2016), 1650100  crossref  mathscinet  zmath  isi  scopus
    10. Speh B., Zhang G., “Restriction to symmetric subgroups of unitary representations of rank one semisimple Lie groups”, Math. Z., 283:1-2 (2016), 629–647  crossref  mathscinet  zmath  isi  elib  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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