Computation of partition functions of free fermionic solvable lattice models via permutation graphs

TL;DR

This paper presents a new general method using permutation graphs and F-matrices to compute partition functions of free fermionic solvable lattice models, extending to models related to Cartan types B and C.

Contribution

Introduction of a permutation graph-based method for calculating partition functions, applicable to broader classes of lattice models including those related to Cartan types B and C.

Findings

Applicable to ice models related to Tokuyama's formula

Able to compute Whittaker functions on metaplectic covers

Generalizes existing methods to new lattice models

Abstract

In this paper, we introduce a novel and general method for computing partition functions of solvable lattice models with free fermionic Boltzmann weights. The method is based on the ``permutation graph'' and the ``$F$-matrix'': the permutation graph is a generalization of the $R$-matrix, and the $F$-matrix is constructed based on the permutation graph. The method allows generalizations to lattice models that are related to Cartan types B and C. Two applications are presented: they involve an ice model related to Tokuyama's formula and another ice model representing a Whittaker function on the metaplectic double cover of $\mathrm{Sp}(2r,F)$ with $F$ being a non-archimedean local field.