Results

**1 - 3**of**3**### ON A FAMILY OF SYMMETRIC RATIONAL FUNCTIONS

"... Abstract. 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 P and Q Hall-Littlewood polynomials. We establish (a) a combinatorial ..."

Abstract
- Add to MetaCart

(Show Context)
Abstract. 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 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

### The domain wall partition function for the Izergin-Korepin 19-vertex model at a root of unity

"... We study the domain wall partition function ZN for the Uq(A (2) 2) (Izergin-Korepin) integrable 19-vertex model on a square lattice of size N. ZN is a symmetric function of two sets of parameters: horizontal ζ1,.., ζN and vertical z1,.., zN rapidities. For generic values of the parameter q we derive ..."

Abstract
- Add to MetaCart

(Show Context)
We study the domain wall partition function ZN for the Uq(A (2) 2) (Izergin-Korepin) integrable 19-vertex model on a square lattice of size N. ZN is a symmetric function of two sets of parameters: horizontal ζ1,.., ζN and vertical z1,.., zN rapidities. For generic values of the parameter q we derive the recurrence relation for the domain wall partition function relating ZN+1 to PNZN, where PN is the proportionality factor in the recurrence, which is a polynomial symmetric in two sets of variables ζ1,.., ζN and z1,.., zN. After setting q 3 = −1 the recurrence relation simplifies and we solve it in terms of a Jacobi-Trudi-like determinant of polynomials generated by PN. 1

### Multivariate quadratic transformations and the interpolation kernel

, 2014

"... ar ..."

(Show Context)