Symmetric functions from wavefunctions of the six-vertex model with triangular boundary

Kohei Motegi

Published 2017-03-23Version 1

We introduce and study a class of partition functions of integrable lattice models with triangular boundary. By using the $U_q(sl_2)$ $R$-matrix and a special class of the triangular $K$-matrix, we first introduce an analogue of the wavefunctions of the integrable six-vertex model with triangular boundary. We give a characterization of the wavefunctions by extending our recent work of the Izergin-Korepin analysis of the domain wall boundary partition function with triangular boundary. We determine the explicit form of the symmetric functions representing the wavefunctions by showing that it satisfies all the required properties.