Identity between Restricted Cauchy Sums for the $q$-Whittaker and Skew Schur Polynomials
SIGMA 20 (2024), 064, 28 pages The Cauchy identities play an important role in the theory of symmetric functions. It is known that Cauchy sums for the $q$-Whittaker and the skew Schur polynomials produce the same factorized expressions modulo a $q$-Pochhammer symbol. We consider the sums with restri...
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| creator | Imamura, Takashi Mucciconi, Matteo Sasamoto, Tomohiro |
| description | SIGMA 20 (2024), 064, 28 pages The Cauchy identities play an important role in the theory of symmetric
functions. It is known that Cauchy sums for the $q$-Whittaker and the skew
Schur polynomials produce the same factorized expressions modulo a
$q$-Pochhammer symbol. We consider the sums with restrictions on the length of
the first rows for labels of both polynomials and prove an identity which
relates them. The proof is based on techniques from integrable probability: we
rewrite the identity in terms of two probability measures: the $q$-Whittaker
measure and the periodic Schur measure. The relation follows by comparing their
Fredholm determinant formulas. |
| doi_str_mv | 10.48550/arxiv.2106.11913 |
| format | Article |
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functions. It is known that Cauchy sums for the $q$-Whittaker and the skew
Schur polynomials produce the same factorized expressions modulo a
$q$-Pochhammer symbol. We consider the sums with restrictions on the length of
the first rows for labels of both polynomials and prove an identity which
relates them. The proof is based on techniques from integrable probability: we
rewrite the identity in terms of two probability measures: the $q$-Whittaker
measure and the periodic Schur measure. The relation follows by comparing their
Fredholm determinant formulas.</description><identifier>DOI: 10.48550/arxiv.2106.11913</identifier><language>eng</language><subject>Mathematics - Combinatorics ; Mathematics - Mathematical Physics ; Mathematics - Probability ; Physics - Mathematical Physics</subject><creationdate>2021-06</creationdate><rights>http://creativecommons.org/licenses/by-sa/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2106.11913$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2106.11913$$DView paper in arXiv$$Hfree_for_read</backlink><backlink>$$Uhttps://doi.org/10.3842/SIGMA.2024.064$$DView published paper (Access to full text may be restricted)$$Hfree_for_read</backlink></links><search><creatorcontrib>Imamura, Takashi</creatorcontrib><creatorcontrib>Mucciconi, Matteo</creatorcontrib><creatorcontrib>Sasamoto, Tomohiro</creatorcontrib><title>Identity between Restricted Cauchy Sums for the $q$-Whittaker and Skew Schur Polynomials</title><description>SIGMA 20 (2024), 064, 28 pages The Cauchy identities play an important role in the theory of symmetric
functions. It is known that Cauchy sums for the $q$-Whittaker and the skew
Schur polynomials produce the same factorized expressions modulo a
$q$-Pochhammer symbol. We consider the sums with restrictions on the length of
the first rows for labels of both polynomials and prove an identity which
relates them. The proof is based on techniques from integrable probability: we
rewrite the identity in terms of two probability measures: the $q$-Whittaker
measure and the periodic Schur measure. The relation follows by comparing their
Fredholm determinant formulas.</description><subject>Mathematics - Combinatorics</subject><subject>Mathematics - Mathematical Physics</subject><subject>Mathematics - Probability</subject><subject>Physics - Mathematical Physics</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotz89LwzAYxvFcPMj0D_C0HHZtbZo2SY9S_DEYTOxg3sqb5C0NW1tNU2f_e-cUHvjeHvgQcseSOFN5ntyD_3ZfccoSETNWMH5N3tcW--DCTDWGE2JP33AM3pmAlpYwmXam1dSNtBk8DS3S1ecq2rcuBDigp9BbWh3wRCvTTp6-Dse5HzoHx_GGXDXn4O1_F2T39LgrX6LN9nldPmwiEJJHuZJcc5Vyc15mhEAFGQcLBYKRuU40R6kKJljTSIZaJ1bYNJWcF0oaY_iCLP9uL7T6w7sO_Fz_EusLkf8AxFpMQQ</recordid><startdate>20210622</startdate><enddate>20210622</enddate><creator>Imamura, Takashi</creator><creator>Mucciconi, Matteo</creator><creator>Sasamoto, Tomohiro</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20210622</creationdate><title>Identity between Restricted Cauchy Sums for the $q$-Whittaker and Skew Schur Polynomials</title><author>Imamura, Takashi ; Mucciconi, Matteo ; Sasamoto, Tomohiro</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a673-5873b3823c23c4c66e8a43ada9eac75b0b3e789161ff71ebb0d6d22733987ccc3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Mathematics - Combinatorics</topic><topic>Mathematics - Mathematical Physics</topic><topic>Mathematics - Probability</topic><topic>Physics - Mathematical Physics</topic><toplevel>online_resources</toplevel><creatorcontrib>Imamura, Takashi</creatorcontrib><creatorcontrib>Mucciconi, Matteo</creatorcontrib><creatorcontrib>Sasamoto, Tomohiro</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Imamura, Takashi</au><au>Mucciconi, Matteo</au><au>Sasamoto, Tomohiro</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Identity between Restricted Cauchy Sums for the $q$-Whittaker and Skew Schur Polynomials</atitle><date>2021-06-22</date><risdate>2021</risdate><abstract>SIGMA 20 (2024), 064, 28 pages The Cauchy identities play an important role in the theory of symmetric
functions. It is known that Cauchy sums for the $q$-Whittaker and the skew
Schur polynomials produce the same factorized expressions modulo a
$q$-Pochhammer symbol. We consider the sums with restrictions on the length of
the first rows for labels of both polynomials and prove an identity which
relates them. The proof is based on techniques from integrable probability: we
rewrite the identity in terms of two probability measures: the $q$-Whittaker
measure and the periodic Schur measure. The relation follows by comparing their
Fredholm determinant formulas.</abstract><doi>10.48550/arxiv.2106.11913</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Combinatorics Mathematics - Mathematical Physics Mathematics - Probability Physics - Mathematical Physics |
| title | Identity between Restricted Cauchy Sums for the $q$-Whittaker and Skew Schur Polynomials |
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