The 6 Vertex Model and Schubert Polynomials
We enumerate staircases with fixed left and right columns. These objects correspond to ice-configurations, or alternating sign matrices, with fixed top and bottom parts. The resulting partition functions are equal, up to a normalization factor, to some Schubert polynomials.
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2007-02-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://www.emis.de/journals/SIGMA/2007/029/ |
| _version_ | 1818561920224985088 |
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| author | Alain Lascoux |
| author_facet | Alain Lascoux |
| author_sort | Alain Lascoux |
| collection | DOAJ |
| description | We enumerate staircases with fixed left and right columns. These objects correspond to ice-configurations, or alternating sign matrices, with fixed top and bottom parts. The resulting partition functions are equal, up to a normalization factor, to some Schubert polynomials. |
| first_indexed | 2024-12-14T00:57:00Z |
| format | Article |
| id | doaj.art-06dcc3c8a23a4093b7855720999314f5 |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-12-14T00:57:00Z |
| publishDate | 2007-02-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-06dcc3c8a23a4093b7855720999314f52022-12-21T23:23:29ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592007-02-013029The 6 Vertex Model and Schubert PolynomialsAlain LascouxWe enumerate staircases with fixed left and right columns. These objects correspond to ice-configurations, or alternating sign matrices, with fixed top and bottom parts. The resulting partition functions are equal, up to a normalization factor, to some Schubert polynomials.http://www.emis.de/journals/SIGMA/2007/029/alternating sign matricesYoung tableauxstaircasesSchubert polynomialsintegrable systems |
| spellingShingle | Alain Lascoux The 6 Vertex Model and Schubert Polynomials Symmetry, Integrability and Geometry: Methods and Applications alternating sign matrices Young tableaux staircases Schubert polynomials integrable systems |
| title | The 6 Vertex Model and Schubert Polynomials |
| title_full | The 6 Vertex Model and Schubert Polynomials |
| title_fullStr | The 6 Vertex Model and Schubert Polynomials |
| title_full_unstemmed | The 6 Vertex Model and Schubert Polynomials |
| title_short | The 6 Vertex Model and Schubert Polynomials |
| title_sort | 6 vertex model and schubert polynomials |
| topic | alternating sign matrices Young tableaux staircases Schubert polynomials integrable systems |
| url | http://www.emis.de/journals/SIGMA/2007/029/ |
| work_keys_str_mv | AT alainlascoux the6vertexmodelandschubertpolynomials AT alainlascoux 6vertexmodelandschubertpolynomials |