Branching Laws for Some Unitary Representations of SL(4,R)
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...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2008 |
| ISSN: | 1815-0659 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2008
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/148973 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Branching Laws for Some Unitary Representations of SL(4,R) / B. Ørsted, B. Speh // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 28 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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.
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| ISSN: | 1815-0659 |