On Complex Gamma-Function Integrals
It was observed recently that relations between matrix elements of certain operators in the SL(2, ℝ) spin chain models take the form of multidimensional integrals derived by R.A. Gustafson. The spin magnets with SL(2, ℂ) symmetry group and L₂(ℂ) as a local Hilbert space give rise to a new type of Γ-...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2020 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут математики НАН України
2020
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/210607 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | On Complex Gamma-Function Integrals. Sergey É. Derkachov and Alexander N. Manashov. SIGMA 16 (2020), 003, 20 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-210607 |
|---|---|
| record_format |
dspace |
| spelling |
Derkachov, Sergey É. Manashov, Alexander N. 2025-12-12T10:40:53Z 2020 On Complex Gamma-Function Integrals. Sergey É. Derkachov and Alexander N. Manashov. SIGMA 16 (2020), 003, 20 pages 1815-0659 2010 Mathematics Subject Classification: 33C70; 81R12 arXiv:1908.01530 https://nasplib.isofts.kiev.ua/handle/123456789/210607 https://doi.org/10.3842/SIGMA.2020.003 It was observed recently that relations between matrix elements of certain operators in the SL(2, ℝ) spin chain models take the form of multidimensional integrals derived by R.A. Gustafson. The spin magnets with SL(2, ℂ) symmetry group and L₂(ℂ) as a local Hilbert space give rise to a new type of Γ-function integrals. In this work, we present a direct calculation of two such integrals. We also analyse properties of these integrals and show that they comprise the star-triangle relations recently discussed in the literature. It is also shown that in the quasi-classical limit, these integral identities are reduced to the duality relations for Dotsenko-Fateev integrals. We are grateful to A.V. Litvinov and V.P. Spiridonov for fruitful discussions. We would also like to express our sincere gratitude to the referees for their numerous useful comments and suggestions. This study was supported by the Russian Science Foundation project No 19-1100131 and Deutsche Forschungsgemeinschaft (A.M.), grant MO 1801/1-3. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On Complex Gamma-Function Integrals Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
On Complex Gamma-Function Integrals |
| spellingShingle |
On Complex Gamma-Function Integrals Derkachov, Sergey É. Manashov, Alexander N. |
| title_short |
On Complex Gamma-Function Integrals |
| title_full |
On Complex Gamma-Function Integrals |
| title_fullStr |
On Complex Gamma-Function Integrals |
| title_full_unstemmed |
On Complex Gamma-Function Integrals |
| title_sort |
on complex gamma-function integrals |
| author |
Derkachov, Sergey É. Manashov, Alexander N. |
| author_facet |
Derkachov, Sergey É. Manashov, Alexander N. |
| publishDate |
2020 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
It was observed recently that relations between matrix elements of certain operators in the SL(2, ℝ) spin chain models take the form of multidimensional integrals derived by R.A. Gustafson. The spin magnets with SL(2, ℂ) symmetry group and L₂(ℂ) as a local Hilbert space give rise to a new type of Γ-function integrals. In this work, we present a direct calculation of two such integrals. We also analyse properties of these integrals and show that they comprise the star-triangle relations recently discussed in the literature. It is also shown that in the quasi-classical limit, these integral identities are reduced to the duality relations for Dotsenko-Fateev integrals.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/210607 |
| citation_txt |
On Complex Gamma-Function Integrals. Sergey É. Derkachov and Alexander N. Manashov. SIGMA 16 (2020), 003, 20 pages |
| work_keys_str_mv |
AT derkachovsergeye oncomplexgammafunctionintegrals AT manashovalexandern oncomplexgammafunctionintegrals |
| first_indexed |
2025-12-17T12:04:19Z |
| last_indexed |
2025-12-17T12:04:19Z |
| _version_ |
1851756966725025792 |