Symmetry breaking for representations of rank one orthogonal groups:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
2015
|
| Series: | Memoirs of the American Mathematical Society
1126 |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | "Volume 238, number 1126 (fourth of 6 numbers), November 2015." |
| Physical Description: | V, 112 S. |
| ISBN: | 9781470419226 |
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MARC
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| 100 | 1 | |a Kobayashi, Toshiyuki |d 1962- |e Verfasser |0 (DE-588)134051513 |4 aut | |
| 245 | 1 | 0 | |a Symmetry breaking for representations of rank one orthogonal groups |c Toshiyuki Kobayashi, Birgit Speh |
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2015 | |
| 300 | |a V, 112 S. | ||
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| 490 | 1 | |a Memoirs of the American Mathematical Society |v 1126 = Vol. 238,4 | |
| 500 | |a "Volume 238, number 1126 (fourth of 6 numbers), November 2015." | ||
| 700 | 1 | |a Speh, Birgit |d 1949- |e Verfasser |0 (DE-588)1078376727 |4 aut | |
| 830 | 0 | |a Memoirs of the American Mathematical Society |v 1126 |w (DE-604)BV008000141 |9 1126 | |
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Record in the Search Index
| _version_ | 1804175702794174464 |
|---|---|
| adam_text | Contents
Chapter 1. Introduction I
Chapter 2. Symmetry breaking for the spherical principal series
representations 11
2.1. Notation and review of previous results 11
2.2. Finite-dimensional subquotients of disconnected groups 13
2.3. Symmetry breaking operators and spherical principal series
representations 14
2.4. Multiplicities for composition factors 19
Chapter 3. Symmetry breaking operators 23
3.1. Restriction of representations and symmetry breaking operators 23
3.2. Distribution kernels of symmetry breaking operators 23
3.3. Differential intertwining operators 26
3.4. Smooth representations and intertwining operators 28
3.5. Symmetry breaking operators for principal series representations 29
3.6. Meromorphic continuation of symmetry breaking operators 30
Chapter 4. More about principal series representations 33
4.1. Models of principal series representations 33
4.2. Explicit AT-finite functions in the non-compact model 36
4.3. Normalized Knapp-Stein intertwining operator 37
Chapter 5. Double coset decomposition P* G/P 41
Chapter 6. Differential equations satisfied by the distribution kernels of
symmetry breaking operators 45
6.1. A system of differential equations for symmetry breaking operators 45
6.2. The solutions «Soi(Rn — {0}; A, u) 46
Chapter 7. AT-finite vectors and regular symmetry breaking operators A49
7.1. Distribution kernel Kyv and its normalization 49
7.2. Preliminary results 51
7.3. Proof of Proposition 7.3 53
Chapter 8. Meromorphic continuation of regular symmetry breaking operators
K , 57
8.1. Recurrence relations of the distribution kernels Kyu 57
8.2. Functional equations 59
8.3. 8.3 Support of K* y 60
lii
IV
CONTENTS
8.4. Renormalization A ^u for v G —N 61
Chapter 9. Singular symmetry breaking operator № u 63
9.1. Singular symmetry breaking operator B ։L/ 63
9.2. iC-finite vectors and singular operators 65
9.3. Proof of Theorem 9.1 _ 66
9.4. Support of the distribution kernel of Ba l, 66
9.5. Renormalization Ba,i/ for (A, u) 6 TeVen with n odd 66
Chapter 10. Differential symmetry breaking operators 69
10.1. Power of the Laplacian 69
10.2. JuhPs family of differential operators 70
10.3. The kernel of the differential symmetry breaking operator C tU 72
Chapter 11. Classification of symmetry breaking operators 75
11.1. Classification of symmetry breaking operators 75
11.2. Strategy of the proof of Theorem 11.1 76
11.3. Lower bounds of the multiplicities 77
11.4. Extension of solutions from Rn — {0} to Rn 78
11.5. Regular symmetry breaking operators 81
11.6. Singular symmetry breaking operators 81
Chapter 12. Residue formulae and functional identities 83
12.1. Residues of symmetry breaking operators 83
12.2. Functional equations satisfied by singular symmetry breaking
operators 85
Chapter 13. Image of symmetry breaking operators 89
13.1. Finite-dimensional image for v € —N 89
13.2. Image for u G m -l· N 90
13.3. Spherical vectors and symmetry breaking operators 91
Chapter 14. Application to analysis on anti-de Sitter space 93
14.1. Harmonic analysis on Lorentzian hyperbolic spaces 93
14.2. Application of symmetry breaking operators to anti-de Sitter spaces 94
14.3. Analysis on vector bundles over anti-de Sitter spaces 98
Chapter 15. Application to branching laws of complementary series 101
15.1. Discrete spectrum in complementary series 101
15.2. JL2-model of complementary series representations 101
Chapter 16. Appendix 105
16.1. Gegenbauer polynomials 105
16.2. A -Bessel function and its renormalization 106
16.3. Zuckerman derived functor modules Aq(A) 106
Acknowledgments 108
References 109
List of Symbols 111
|
| any_adam_object | 1 |
| author | Kobayashi, Toshiyuki 1962- Speh, Birgit 1949- |
| author_GND | (DE-588)134051513 (DE-588)1078376727 |
| author_facet | Kobayashi, Toshiyuki 1962- Speh, Birgit 1949- |
| author_role | aut aut |
| author_sort | Kobayashi, Toshiyuki 1962- |
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| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.482 512.482 |
| dewey-search | 512/.482 512.482 |
| dewey-sort | 3512 3482 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV043206168 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:20:29Z |
| institution | BVB |
| isbn | 9781470419226 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028629380 |
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| physical | V, 112 S. |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Kobayashi, Toshiyuki 1962- Verfasser (DE-588)134051513 aut Symmetry breaking for representations of rank one orthogonal groups Toshiyuki Kobayashi, Birgit Speh Providence, RI American Math. Soc. 2015 V, 112 S. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 1126 = Vol. 238,4 "Volume 238, number 1126 (fourth of 6 numbers), November 2015." Speh, Birgit 1949- Verfasser (DE-588)1078376727 aut Memoirs of the American Mathematical Society 1126 (DE-604)BV008000141 1126 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028629380&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kobayashi, Toshiyuki 1962- Speh, Birgit 1949- Symmetry breaking for representations of rank one orthogonal groups Memoirs of the American Mathematical Society |
| title | Symmetry breaking for representations of rank one orthogonal groups |
| title_auth | Symmetry breaking for representations of rank one orthogonal groups |
| title_exact_search | Symmetry breaking for representations of rank one orthogonal groups |
| title_full | Symmetry breaking for representations of rank one orthogonal groups Toshiyuki Kobayashi, Birgit Speh |
| title_fullStr | Symmetry breaking for representations of rank one orthogonal groups Toshiyuki Kobayashi, Birgit Speh |
| title_full_unstemmed | Symmetry breaking for representations of rank one orthogonal groups Toshiyuki Kobayashi, Birgit Speh |
| title_short | Symmetry breaking for representations of rank one orthogonal groups |
| title_sort | symmetry breaking for representations of rank one orthogonal groups |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028629380&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
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