On a family of symmetric rational functions
This paper is about a family of symmetric rational functions that form a one-parameter generalization of the classical Hall-Littlewood polynomials. We introduce two sets of (skew and non-skew) functions that are akin to the P and Q Hall-Littlewood polynomials. We establish (a) a combinatorial formul...
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| Format: | Article |
| Language: | English |
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Elsevier BV,
2019-03-05T17:13:40Z.
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| Subjects: | |
| Online Access: | Get fulltext |
| Summary: | This paper is about a family of symmetric rational functions that form a one-parameter generalization of the classical Hall-Littlewood polynomials. We introduce two sets of (skew and non-skew) functions that are akin to the P and Q Hall-Littlewood polynomials. We establish (a) a combinatorial formula that represents our functions as partition functions for certain path ensembles in the square grid; (b) symmetrization formulas for non-skew functions; (c) identities of Cauchy and Pieri type; (d) explicit formulas for principal specializations; (e) two types of orthogonality relations for non-skew functions. Our construction is closely related to the half-infinite volume, finite magnon sector limit of the higher spin six-vertex (or XXZ) model, with both sets of functions representing higher spin six-vertex partition functions and/or transfer-matrices for certain domains. Keywords: Symmetric rational functions National Science Foundation (U.S.) (Grant DMS-1056390) |
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