Multivariate Quadratic Transformations and the Interpolation Kernel
We prove a number of quadratic transformations of elliptic Selberg integrals (conjectured in an earlier paper of the author), as well as studying in depth the "interpolation kernel", an analytic continuation of the author's elliptic interpolation functions which plays a major role in...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2018 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2018
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/209445 |
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| Zitieren: | Multivariate Quadratic Transformations and the Interpolation Kernel / E.M. Rains // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 36 назв. — англ. |
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Rains, E.M. 2025-11-21T18:59:10Z 2018 Multivariate Quadratic Transformations and the Interpolation Kernel / E.M. Rains // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 36 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33D67; 33E05 arXiv: 1408.0305 https://nasplib.isofts.kiev.ua/handle/123456789/209445 https://doi.org/10.3842/SIGMA.2018.019 We prove a number of quadratic transformations of elliptic Selberg integrals (conjectured in an earlier paper of the author), as well as studying in depth the "interpolation kernel", an analytic continuation of the author's elliptic interpolation functions which plays a major role in the proof as well as acting as the kernel for a Fourier transform on certain elliptic double affine Hecke algebras (discussed in a later paper). In the process, we give a number of examples of a new approach to proving elliptic hypergeometric integral identities by reduction to a Zariski dense subset of a formal neighborhood of the trigonometric limit. The author would particularly like to thank P. Etingof for an initial suggestion that taking p to be a formal variable might allow one to extend the W(E7) symmetry of the order 1 elliptic Selberg to W(E8); this turned out not to work (some symmetries are, indeed, gained, but at the expense of others), but led the author to a more general study of the formal limit. In addition, the author would like to thank D. Betea, M. Wheeler, and P. Zinn-Justin for discussions relating to Izergin–Korepin determinants and their elliptic analogues, and especially for discussions relating to Conjecture 1 of [1] (which led the author to consider the general case of the Littlewood kernel below). The author would also like to thank O. Warnaar for additional discussions related to the Macdonald polynomial limit. The author would finally like to thank H. Rosengren for providing extra motivation to finish writing the present work, as well as some helpful pointers to the vertex model literature. The author was partially supported by the National Science Foundation (grant number DMS-1001645). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Multivariate Quadratic Transformations and the Interpolation Kernel Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Multivariate Quadratic Transformations and the Interpolation Kernel |
| spellingShingle |
Multivariate Quadratic Transformations and the Interpolation Kernel Rains, E.M. |
| title_short |
Multivariate Quadratic Transformations and the Interpolation Kernel |
| title_full |
Multivariate Quadratic Transformations and the Interpolation Kernel |
| title_fullStr |
Multivariate Quadratic Transformations and the Interpolation Kernel |
| title_full_unstemmed |
Multivariate Quadratic Transformations and the Interpolation Kernel |
| title_sort |
multivariate quadratic transformations and the interpolation kernel |
| author |
Rains, E.M. |
| author_facet |
Rains, E.M. |
| publishDate |
2018 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We prove a number of quadratic transformations of elliptic Selberg integrals (conjectured in an earlier paper of the author), as well as studying in depth the "interpolation kernel", an analytic continuation of the author's elliptic interpolation functions which plays a major role in the proof as well as acting as the kernel for a Fourier transform on certain elliptic double affine Hecke algebras (discussed in a later paper). In the process, we give a number of examples of a new approach to proving elliptic hypergeometric integral identities by reduction to a Zariski dense subset of a formal neighborhood of the trigonometric limit.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/209445 |
| citation_txt |
Multivariate Quadratic Transformations and the Interpolation Kernel / E.M. Rains // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 36 назв. — англ. |
| work_keys_str_mv |
AT rainsem multivariatequadratictransformationsandtheinterpolationkernel |
| first_indexed |
2025-12-07T20:46:47Z |
| last_indexed |
2025-12-07T20:46:47Z |
| _version_ |
1850886155910774784 |