Orthogonality Relations and Cherednik Identities for Multivariable Baker-Akhiezer Functions
Author Manuscript 27 Feb 2013
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Elsevier
2014
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| Online Access: | http://hdl.handle.net/1721.1/86396 https://orcid.org/0000-0002-0710-1416 |
| _version_ | 1826209080734121984 |
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| author | Chalykh, Oleg Etingof, Pavel I. |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Chalykh, Oleg Etingof, Pavel I. |
| author_sort | Chalykh, Oleg |
| collection | MIT |
| description | Author Manuscript 27 Feb 2013 |
| first_indexed | 2024-09-23T14:16:56Z |
| format | Article |
| id | mit-1721.1/86396 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T14:16:56Z |
| publishDate | 2014 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | mit-1721.1/863962022-09-28T19:43:03Z Orthogonality Relations and Cherednik Identities for Multivariable Baker-Akhiezer Functions Chalykh, Oleg Etingof, Pavel I. Massachusetts Institute of Technology. Department of Mathematics Etingof, Pavel I. Author Manuscript 27 Feb 2013 We establish orthogonality relations for the Baker–Akhiezer (BA) eigenfunctions of the Macdonald difference operators. We also obtain a version of Cherednik–Macdonald–Mehta integral for these functions. As a corollary, we give a simple derivation of the norm identity and Cherednik–Macdonald–Mehta integral for Macdonald polynomials. In the appendix written by the first author, we prove a summation formula for BA functions. We also consider more general identities of Cherednik type, which we use to introduce and construct more general, twisted BA functions. This leads to a construction of new quantum integrable models of Macdonald–Ruijsenaars type. National Science Foundation (U.S.) (Grant DMS-1000113) 2014-05-05T13:05:53Z 2014-05-05T13:05:53Z 2013-03 2011-10 Article http://purl.org/eprint/type/JournalArticle 00018708 1090-2082 http://hdl.handle.net/1721.1/86396 Chalykh, Oleg, and Pavel Etingof. “Orthogonality relations and Cherednik identities for multivariable Baker–Akhiezer functions.” Advances in Mathematics 238 (May 2013): 246-289. https://orcid.org/0000-0002-0710-1416 en_US http://dx.doi.org/10.1016/j.aim.2013.01.010 Advances in Mathematics application/pdf Elsevier arXiv |
| spellingShingle | Chalykh, Oleg Etingof, Pavel I. Orthogonality Relations and Cherednik Identities for Multivariable Baker-Akhiezer Functions |
| title | Orthogonality Relations and Cherednik Identities for Multivariable Baker-Akhiezer Functions |
| title_full | Orthogonality Relations and Cherednik Identities for Multivariable Baker-Akhiezer Functions |
| title_fullStr | Orthogonality Relations and Cherednik Identities for Multivariable Baker-Akhiezer Functions |
| title_full_unstemmed | Orthogonality Relations and Cherednik Identities for Multivariable Baker-Akhiezer Functions |
| title_short | Orthogonality Relations and Cherednik Identities for Multivariable Baker-Akhiezer Functions |
| title_sort | orthogonality relations and cherednik identities for multivariable baker akhiezer functions |
| url | http://hdl.handle.net/1721.1/86396 https://orcid.org/0000-0002-0710-1416 |
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