Matrix product and sum rule for Macdonald polynomials
We present a new, explicit sum formula for symmetric Macdonald polynomials Pλ and show that they can be written as a trace over a product of (infinite dimensional) matrices. These matrices satisfy the Zamolodchikov– Faddeev (ZF) algebra. We construct solutions of the ZF algebra from a rank-reduced v...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2020-04-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/6419/pdf |
| _version_ | 1797270213890146304 |
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| author | Luigi Cantini Jan De Gier Michael Wheeler |
| author_facet | Luigi Cantini Jan De Gier Michael Wheeler |
| author_sort | Luigi Cantini |
| collection | DOAJ |
| description | We present a new, explicit sum formula for symmetric Macdonald polynomials Pλ and show that they can be written as a trace over a product of (infinite dimensional) matrices. These matrices satisfy the Zamolodchikov– Faddeev (ZF) algebra. We construct solutions of the ZF algebra from a rank-reduced version of the Yang–Baxter algebra. As a corollary, we find that the normalization of the stationary measure of the multi-species asymmetric exclusion process is a Macdonald polynomial with all variables set equal to one. |
| first_indexed | 2024-04-25T02:00:42Z |
| format | Article |
| id | doaj.art-86be2151ee274ea19fa883585452f844 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:00:42Z |
| publishDate | 2020-04-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-86be2151ee274ea19fa883585452f8442024-03-07T14:55:20ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502020-04-01DMTCS Proceedings, 28th...10.46298/dmtcs.64196419Matrix product and sum rule for Macdonald polynomialsLuigi Cantini0Jan De GierMichael Wheeler1https://orcid.org/0000-0001-5403-3914Laboratoire de Physique Théorique et ModélisationDepartment of Mathematics and Statistics [Melbourne]We present a new, explicit sum formula for symmetric Macdonald polynomials Pλ and show that they can be written as a trace over a product of (infinite dimensional) matrices. These matrices satisfy the Zamolodchikov– Faddeev (ZF) algebra. We construct solutions of the ZF algebra from a rank-reduced version of the Yang–Baxter algebra. As a corollary, we find that the normalization of the stationary measure of the multi-species asymmetric exclusion process is a Macdonald polynomial with all variables set equal to one.https://dmtcs.episciences.org/6419/pdf[math.math-co]mathematics [math]/combinatorics [math.co] |
| spellingShingle | Luigi Cantini Jan De Gier Michael Wheeler Matrix product and sum rule for Macdonald polynomials Discrete Mathematics & Theoretical Computer Science [math.math-co]mathematics [math]/combinatorics [math.co] |
| title | Matrix product and sum rule for Macdonald polynomials |
| title_full | Matrix product and sum rule for Macdonald polynomials |
| title_fullStr | Matrix product and sum rule for Macdonald polynomials |
| title_full_unstemmed | Matrix product and sum rule for Macdonald polynomials |
| title_short | Matrix product and sum rule for Macdonald polynomials |
| title_sort | matrix product and sum rule for macdonald polynomials |
| topic | [math.math-co]mathematics [math]/combinatorics [math.co] |
| url | https://dmtcs.episciences.org/6419/pdf |
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