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Restriction of Most Degenerate Representations of O(1,N) with Respect to Symmetric Pairs
http://hdl.handle.net/2261/59271
http://hdl.handle.net/2261/59271c16cedbf-570f-45eb-a0c9-2f86c7ed70ec
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
jms220110.pdf (375.6 kB)
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| Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
|---|---|---|---|---|---|---|
| 公開日 | 2016-03-03 | |||||
| タイトル | ||||||
| タイトル | Restriction of Most Degenerate Representations of O(1,N) with Respect to Symmetric Pairs | |||||
| 言語 | ||||||
| 言語 | eng | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | Unitary representation | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | complementary series | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | principal series | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | discrete series | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | branching law | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | Bessel operators | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | hypergeometric function | |||||
| キーワード | ||||||
| 主題Scheme | Other | |||||
| 主題 | Kodaira–Titchmarsh formula | |||||
| 資源タイプ | ||||||
| 資源 | http://purl.org/coar/resource_type/c_6501 | |||||
| タイプ | departmental bulletin paper | |||||
| 著者 |
Möllers, Jan
× Möllers, Jan× Oshima, Yoshiki |
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| 著者所属 | ||||||
| 著者所属 | Department of Mathematics, The Ohio State University | |||||
| 著者所属 | ||||||
| 著者所属 | Kavli IPMU (WPI), The University of Tokyo | |||||
| 抄録 | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | We find the complete branching law for the restriction of certain unitary representations of O(1, n+1)to the subgroups O(1,m + 1) × O(n − m) , 0≤ m ≤ n. The unitary representations we consider are those induced from a character of a parabolic subgroup or its irreducible quotient. They belong either to the unitary spherical principal series, the spherical complementary series or discrete series for the hyperboloid. In the crucial case 0 < m < n the decomposition consists of a continuous part and a discrete part. The continuous part is given by a direct integral of unitary principal series representations whereas the discrete part consists of finitely many representations which either belong to the complementary series or are discrete series for the hyperboloid. The explicit Plancherel formula is computed on the Fourier transformed side of the non-compact realization of the representations by using the spectral decomposition of a certain hypergeometric type ordinary differential operator. The main tool connecting this differential operator with the representations are second order Bessel operators which describe the Lie algebra action in this realization. To derive the spectral decomposition of the ordinary differential operator we use Kodaira’s formula for the spectral decomposition of Schr¨odinger type operators. | |||||
| 書誌情報 |
Journal of mathematical sciences, the University of Tokyo 巻 22, 号 1, p. 279-338, 発行日 2015-02-27 |
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| ISSN | ||||||
| 収録物識別子タイプ | ISSN | |||||
| 収録物識別子 | 13405705 | |||||
| 書誌レコードID | ||||||
| 収録物識別子タイプ | NCID | |||||
| 収録物識別子 | AA11021653 | |||||
| 日本十進分類法 | ||||||
| 主題Scheme | NDC | |||||
| 主題 | 415 | |||||
| Mathematical Reviews Number | ||||||
| MR | ||||||
| Mathmatical Subject Classification | ||||||
| 22E46(MSC2010) | ||||||
| Mathmatical Subject Classification | ||||||
| 33C05(MSC2010) | ||||||
| Mathmatical Subject Classification | ||||||
| 34B24(MSC2010) | ||||||
| 出版者 | ||||||
| 出版者 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||
| 原稿受領日 | ||||||
| 2014-06-24 | ||||||
