On a family of symmetric rational functions
Author(s)
Borodin, Alexei
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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
Date issued
2016-11Department
Massachusetts Institute of Technology. Department of MathematicsJournal
Advances in Mathematics
Publisher
Elsevier BV
Citation
Borodin, Alexei. “On a Family of Symmetric Rational Functions.” Advances in Mathematics 306 (January 2017): 973–1018 © 2016 Elsevier Inc
Version: Original manuscript
ISSN
0001-8708
1090-2082