A Littlewood-type identity for Robbins polynomials
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910943556927488 |
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| author | Fischer, Ilse Höngesberg, Hans |
| author_facet | Fischer, Ilse Höngesberg, Hans |
| contents | We provide a generalization of the Littlewood identity, both sides of which are related to alternating sign matrices. The classical Littlewood identity establishes a nice product formula for the sum of all Schur polynomials. Compared to the classical identity, Schur polynomials are replaced by so-called modified Robbins polynomials. These polynomials are a generalization of Schur polynomials and enumerate down-arrowed monotone triangles, and thus also alternating sign matrices. As an additional factor on the other side of the identity, we have a Pfaffian formula which we interpret in terms of the partition function of six-vertex model configurations corresponding to diagonally symmetric alternating sign matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_09275 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Littlewood-type identity for Robbins polynomials Fischer, Ilse Höngesberg, Hans Combinatorics 05A05, 05A15, 05A19, 05E05, 82B20 We provide a generalization of the Littlewood identity, both sides of which are related to alternating sign matrices. The classical Littlewood identity establishes a nice product formula for the sum of all Schur polynomials. Compared to the classical identity, Schur polynomials are replaced by so-called modified Robbins polynomials. These polynomials are a generalization of Schur polynomials and enumerate down-arrowed monotone triangles, and thus also alternating sign matrices. As an additional factor on the other side of the identity, we have a Pfaffian formula which we interpret in terms of the partition function of six-vertex model configurations corresponding to diagonally symmetric alternating sign matrices. |
| title | A Littlewood-type identity for Robbins polynomials |
| topic | Combinatorics 05A05, 05A15, 05A19, 05E05, 82B20 |
| url | https://arxiv.org/abs/2505.09275 |