Calogero-Sutherland-type quantum systems, generalized hypergeometric functions and superintegrability for integral chains
Abstract We reinvestigate the Calogero-Sutherland-type (CS-type) models and generalized hypergeometric functions. We construct the generalized CS operators for circular, Hermite, Laguerre, Jacobi and Bessel cases and establish the generalized Lassalle-Nekrasov correspondence. A family of operators a...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-08-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP08(2025)144 |
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| _version_ | 1849226732617334784 |
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| author | Fan Liu Rui Wang Jie Yang Wei-Zhong Zhao |
| author_facet | Fan Liu Rui Wang Jie Yang Wei-Zhong Zhao |
| author_sort | Fan Liu |
| collection | DOAJ |
| description | Abstract We reinvestigate the Calogero-Sutherland-type (CS-type) models and generalized hypergeometric functions. We construct the generalized CS operators for circular, Hermite, Laguerre, Jacobi and Bessel cases and establish the generalized Lassalle-Nekrasov correspondence. A family of operators are constructed based on the spherical degenerate double affine Hecke algebra. In terms of these operators, we provide concise representations and constraints for the generalized hypergeometric functions. We analyze the superintegrability for the β-deformed integrals, where the measures are associated with the corresponding ground state wave functions of Hermite, Laguerre, Jacobi and Bessel type CS models. Then based on the generalized Laplace transformation of Jack polynomials, we construct certain two integral chains and analyze the superintegrability property. |
| format | Article |
| id | doaj-art-934f5f1f46644cc09d80b6097e7fca21 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-934f5f1f46644cc09d80b6097e7fca212025-08-24T11:04:39ZengSpringerOpenJournal of High Energy Physics1029-84792025-08-012025813110.1007/JHEP08(2025)144Calogero-Sutherland-type quantum systems, generalized hypergeometric functions and superintegrability for integral chainsFan Liu0Rui Wang1Jie Yang2Wei-Zhong Zhao3School of Mathematical Sciences, Capital Normal UniversityDepartment of Mathematics, China University of Mining and TechnologySchool of Mathematical Sciences, Capital Normal UniversitySchool of Mathematical Sciences, Capital Normal UniversityAbstract We reinvestigate the Calogero-Sutherland-type (CS-type) models and generalized hypergeometric functions. We construct the generalized CS operators for circular, Hermite, Laguerre, Jacobi and Bessel cases and establish the generalized Lassalle-Nekrasov correspondence. A family of operators are constructed based on the spherical degenerate double affine Hecke algebra. In terms of these operators, we provide concise representations and constraints for the generalized hypergeometric functions. We analyze the superintegrability for the β-deformed integrals, where the measures are associated with the corresponding ground state wave functions of Hermite, Laguerre, Jacobi and Bessel type CS models. Then based on the generalized Laplace transformation of Jack polynomials, we construct certain two integral chains and analyze the superintegrability property.https://doi.org/10.1007/JHEP08(2025)144Integrable HierarchiesMatrix Models |
| spellingShingle | Fan Liu Rui Wang Jie Yang Wei-Zhong Zhao Calogero-Sutherland-type quantum systems, generalized hypergeometric functions and superintegrability for integral chains Journal of High Energy Physics Integrable Hierarchies Matrix Models |
| title | Calogero-Sutherland-type quantum systems, generalized hypergeometric functions and superintegrability for integral chains |
| title_full | Calogero-Sutherland-type quantum systems, generalized hypergeometric functions and superintegrability for integral chains |
| title_fullStr | Calogero-Sutherland-type quantum systems, generalized hypergeometric functions and superintegrability for integral chains |
| title_full_unstemmed | Calogero-Sutherland-type quantum systems, generalized hypergeometric functions and superintegrability for integral chains |
| title_short | Calogero-Sutherland-type quantum systems, generalized hypergeometric functions and superintegrability for integral chains |
| title_sort | calogero sutherland type quantum systems generalized hypergeometric functions and superintegrability for integral chains |
| topic | Integrable Hierarchies Matrix Models |
| url | https://doi.org/10.1007/JHEP08(2025)144 |
| work_keys_str_mv | AT fanliu calogerosutherlandtypequantumsystemsgeneralizedhypergeometricfunctionsandsuperintegrabilityforintegralchains AT ruiwang calogerosutherlandtypequantumsystemsgeneralizedhypergeometricfunctionsandsuperintegrabilityforintegralchains AT jieyang calogerosutherlandtypequantumsystemsgeneralizedhypergeometricfunctionsandsuperintegrabilityforintegralchains AT weizhongzhao calogerosutherlandtypequantumsystemsgeneralizedhypergeometricfunctionsandsuperintegrabilityforintegralchains |