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...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2008 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2008
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/148973 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862710964970848256 |
|---|---|
| author | Ørsted, B. Speh, B. |
| author_facet | Ørsted, B. Speh, B. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
|
| first_indexed | 2025-12-07T17:27:47Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148973 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:27:47Z |
| publishDate | 2008 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Ørsted, B. Speh, B. 2019-02-19T12:19:09Z 2019-02-19T12:19:09Z 2008 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 https://nasplib.isofts.kiev.ua/handle/123456789/148973 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. This paper is a contribution to the Proceedings of the 2007 Midwest Geometry Conference in honor of Thomas P. Branson. We would like to thank T. Kobayashi for helpful discussions during a visit of the second author at RIMS and for the suggestion to also include the restriction to GL(2, C). The second author would also like to thank the University of Southern Denmark in Odense for its hospitality during which part of the research was completed. BS partially supported by NSF grant DMS-0070561. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Branching Laws for Some Unitary Representations of SL(4,R) Article published earlier |
| spellingShingle | Branching Laws for Some Unitary Representations of SL(4,R) Ørsted, B. Speh, B. |
| title | 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_short | Branching Laws for Some Unitary Representations of SL(4,R) |
| title_sort | branching laws for some unitary representations of sl(4,r) |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148973 |
| work_keys_str_mv | AT ørstedb branchinglawsforsomeunitaryrepresentationsofsl4r AT spehb branchinglawsforsomeunitaryrepresentationsofsl4r |