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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2024 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2024
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| Онлайн доступ: | 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 |
| Цитувати: | 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 |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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 |