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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| Datum: | 2008 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2008
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/148973 |
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| 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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irk-123456789-1489732019-02-20T01:25:29Z Branching Laws for Some Unitary Representations of SL(4,R) Ørsted, B. Speh, B. 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. 2008 Article 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. 1815-0659 2000 Mathematics Subject Classification: 22E47; 11F70 http://dspace.nbuv.gov.ua/handle/123456789/148973 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
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. |
| format |
Article |
| author |
Ørsted, B. Speh, B. |
| spellingShingle |
Ørsted, B. Speh, B. Branching Laws for Some Unitary Representations of SL(4,R) Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Ørsted, B. Speh, B. |
| author_sort |
Ørsted, B. |
| title |
Branching Laws for Some Unitary Representations of SL(4,R) |
| title_short |
Branching Laws for Some Unitary Representations of SL(4,R) |
| title_full |
Branching Laws for Some Unitary Representations of SL(4,R) |
| title_fullStr |
Branching Laws for Some Unitary Representations of SL(4,R) |
| title_full_unstemmed |
Branching Laws for Some Unitary Representations of SL(4,R) |
| title_sort |
branching laws for some unitary representations of sl(4,r) |
| publisher |
Інститут математики НАН України |
| publishDate |
2008 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148973 |
| citation_txt |
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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT ørstedb branchinglawsforsomeunitaryrepresentationsofsl4r AT spehb branchinglawsforsomeunitaryrepresentationsofsl4r |
| first_indexed |
2025-07-12T20:48:19Z |
| last_indexed |
2025-07-12T20:48:19Z |
| _version_ |
1837475613894508544 |