Identity between Restricted Cauchy Sums for the -Whittaker and Skew Schur Polynomials
The Cauchy identities play an important role in the theory of symmetric functions. It is known that Cauchy sums for the -Whittaker and the skew Schur polynomials produce the same factorized expressions modulo a -Pochhammer symbol. We consider sums with restrictions on the length of the first rows of...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2024 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2024
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212356 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Identity between Restricted Cauchy Sums for the -Whittaker and Skew Schur Polynomials. Takashi Imamura, Matteo Mucciconi and Tomohiro Sasamoto. SIGMA 20 (2024), 064, 28 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | The Cauchy identities play an important role in the theory of symmetric functions. It is known that Cauchy sums for the -Whittaker and the skew Schur polynomials produce the same factorized expressions modulo a -Pochhammer symbol. We consider sums with restrictions on the length of the first rows of the labels for both polynomials and prove an identity relating them. The proof is based on techniques from integrable probability: we rewrite the identity in terms of two probability measures: the -Whittaker measure and the periodic Schur measure. The relation follows by comparing their Fredholm determinant formulas.
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| ISSN: | 1815-0659 |