Geometry of q-hypergeometric functions, quantum affine algebras and elliptic quantum groups:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Paris
Soc. Math. de France
1997
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| Schriftenreihe: | Astérisque
246 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VI, 135 S. |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text | 246 ASTERISQUE 1997 GEOMETRY OF 4-HYPERGEOMETRIC FUNCTIONS, QUANTUM
AFFINE ALGEBRAS AND ELLIPTIC QUANTUM GROUPS V. TARASOV, A. VARCHENKO
SOCIETE MATHEMATIQUE DE FRANCE PUBLIE AVEC LE CONCOURS DU CENTRE
NATIONAL DE LA RECHERCHE SCIENTIFIQUE CONTENTS 1. INTRODUCTION 1 2.
DISCRETE FLAT CONNECTIONS AND LOCAL SYSTEMS 7 DISCRETE FLAT CONNECTIONS
7 DISCRETE GAUSS-MANIN CONNECTION 9 CONNECTION COEFFICIENTS OF LOCAL
SYSTEMS 11 THE FUNCTIONAL SPACE OF A TRIGONOMETRIC SL2 LOCAL SYSTEM 12
BASES IN THE TRIGONOMETRIC HYPERGEOMETRIC SPACE OF A FIBER 15 THE
ELLIPTIC HYPERGEOMETRIC SPACE 19 3. .R-MATRICES AND THE QKZ CONNECTION
27 HIGHEST WEIGHT C/ G (S[2)-MODULESS 27 THE TRIGONOMETRIC I?-MATRIX 28
THE QUANTUM LOOP ALGEBRA U Q {QL 2 ) 30 THE TRIGONOMETRIC QKZ
CONNECTION ASSOCIATED WITH SI2 * 32 MODULES OVER THE ELLIPTIC QUANTUM
GROUP I?P ]7 (S I2) AND THE ELLIPTIC .R-MATRICES .. 34 4. TENSOR
COORDINATES ON THE HYPERGEOMETRIC SPACES 3 9 TENSOR COORDINATES ON THE
TRIGONOMETRIC HYPERGEOMETRIC SPACES OF FIBERS .-.-. 39 TENSOR
COORDINATES ON THE ELLIPTIC HYPERGEOMETRIC SPACES OF FIBERS .. 42 TENSOR
PRODUCTS OF THE HYPERGEOMETRIC SPACES 46 5. THE HYPERGEOMETRIC PAIRING
AND THE HYPERGEOMETRIC SOLUTIONS OF THE QKZ EQUATION 49 THE
HYPERGEOMETRIC INTEGRAL 49 DETERMINANT FORMULAE FOR THE HYPERGEOMETRIC
PAIRING . . *. 52 THE HYPERGEOMETRIC SOLUTIONS OF THE QKZ EQUATION 56
THE HYPERGEOMETRIC MAP 58 6. ASYMPTOTIC SOLUTIONS OF THE QKZ EQUATION 63
7. PROOFS 71 PROOF OF LEMMAS 2.22, 2.33 71 PROOF OF LEMMAS 2.23, 2.24 71
VI CONTENTS PROOF OF LEMMA 4.3 71 PROOF OF LEMMA 4.15 73 PROOF OF LEMMAS
4.18, 4.19 75 PROOF OF LEMMA 5.7 76 PROOF OF LEMMA 5.8 76 PROOF OF
THEOREM 5.15 76 PROOF OF LEMMAS 5.16, 5.17 77 PROOF OF THEOREM 6.6 78
PROOF OF THEOREM 6.2 81 PROOF OF THEOREM 5.9 81 PROOF OF THEOREM 5.10 82
PROOF OF THEOREM 5.11 86 PROOF OF THEOREM 5.26 86 PROOF OF THEOREM 5.28
87 PROOF OF THEOREM 5.31 87 APPENDICES A. BASIC FACTS ABOUT THE
TRIGONOMETRIC HYPERGEOMETRIC SPACE . . 89 PROOF OF LEMMA 2.21 90 B.
BASIC FACTS ABOUT THE ELLIPTIC HYPERGEOMETRIC SPACE 97 PROOF OF LEMMA
2.31 99 PROOF OF LEMMA 2.38 101 PROOF OF LEMMA 2.39 102 PROOF OF LEMMA
2.36 : 102 PROOF OF LEMMA 2.37 103 C. THE SHAPOVALOV PAIRINGS OF THE
HYPERGEOMETRIC SPACES OF FIBERS . . ., 105 D. THE G-SELBERG INTEGRAL
113 PROOF OF FORMULA (5.13) 113 E. THE MULTIDIMENSIONAL ASKEY-ROY
FORMULA AND ASKEY S CONJECTURE 121 PROOF OF FORMULA (5.14) :* 121 F. THE
JACKSON INTEGRALS VIA THE HYPERGEOMETRIC INTEGRALS .... 127 G. ONE
USEFUL IDENTITY ..... . .,, 131 REFERENCES 133 ASTFIRISQUE 246
|
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| author | Tarasov, Vitalij O. Varčenko, Aleksandr N. 1949- |
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| language | English |
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| physical | VI, 135 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Soc. Math. de France |
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| series | Astérisque |
| series2 | Astérisque |
| spelling | Tarasov, Vitalij O. Verfasser aut Geometry of q-hypergeometric functions, quantum affine algebras and elliptic quantum groups V. Tarasov ; A. Varchenko Paris Soc. Math. de France 1997 VI, 135 S. txt rdacontent n rdamedia nc rdacarrier Astérisque 246 Hypergeometrische Reihe (DE-588)4161061-1 gnd rswk-swf Hypergeometrische Reihe (DE-588)4161061-1 s DE-604 Varčenko, Aleksandr N. 1949- Verfasser (DE-588)115203257 aut Astérisque 246 (DE-604)BV002579439 246 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008260430&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tarasov, Vitalij O. Varčenko, Aleksandr N. 1949- Geometry of q-hypergeometric functions, quantum affine algebras and elliptic quantum groups Astérisque Hypergeometrische Reihe (DE-588)4161061-1 gnd |
| subject_GND | (DE-588)4161061-1 |
| title | Geometry of q-hypergeometric functions, quantum affine algebras and elliptic quantum groups |
| title_auth | Geometry of q-hypergeometric functions, quantum affine algebras and elliptic quantum groups |
| title_exact_search | Geometry of q-hypergeometric functions, quantum affine algebras and elliptic quantum groups |
| title_full | Geometry of q-hypergeometric functions, quantum affine algebras and elliptic quantum groups V. Tarasov ; A. Varchenko |
| title_fullStr | Geometry of q-hypergeometric functions, quantum affine algebras and elliptic quantum groups V. Tarasov ; A. Varchenko |
| title_full_unstemmed | Geometry of q-hypergeometric functions, quantum affine algebras and elliptic quantum groups V. Tarasov ; A. Varchenko |
| title_short | Geometry of q-hypergeometric functions, quantum affine algebras and elliptic quantum groups |
| title_sort | geometry of q hypergeometric functions quantum affine algebras and elliptic quantum groups |
| topic | Hypergeometrische Reihe (DE-588)4161061-1 gnd |
| topic_facet | Hypergeometrische Reihe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008260430&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002579439 |
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