Journal of Physics Conference Series

Izergin-Korepin approach to symmetric functions

Kohei Motegi, Kazumitsu Sakai

Published Apr 1, 2019• 0 citations

Abstract

Recently, the Izergin-Korepin technique, which was originally a method to the analyze the domain wall boundary partition functions initiated by Korepin and Izergin, was extended to the wavefunctions of integrable six-vertex models. We illustrate for the case of the rational integrable models.

DOI: 10.1088/1742-6596/1194/1/012077

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Journal of Physics Conference Series

Izergin-Korepin approach to symmetric functions

Kohei Motegi, Kazumitsu Sakai

Published Apr 1, 2019• 0 citations

Publisher

Abstract

DOI: 10.1088/1742-6596/1194/1/012077

Related papers

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U_q(sl_2)

R

-matrix and a special class of the triangular

K

-matrix. By using its graphical representation, we make the Izergin-Korepin analysis with the help of the Yang-Baxter relation and the reflection equation to give a characterization of the partition function. The explict form of the symmetric function representing the partition function is presented by showing that it satisfies all the required properties.

We study the domain wall partition function

Z_N

for the

U_q(A_2^{(2)})

(Izergin-Korepin) integrable

19

-vertex model on a square lattice of size

N

Z_N

is a symmetric function of two sets of parameters: horizontal

ζ_1,..,ζ_N

and vertical

z_1,..,z_N

rapidities. For generic values of the parameter

q

we derive the recurrence relation for the domain wall partition function relating

Z_{N+1}

P_N Z_N

, where

P_N

is the proportionality factor in the recurrence, which is a polynomial symmetric in two sets of variables

ζ_1,..,ζ_N

and

z_1,..,z_N

. 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

P_N