Functional equations for transfer-matrix operators in open Hecke chain models

TL;DR

This paper develops functional equations for transfer-matrix operators in open Hecke chain models, extending known relations in solvable spin chains and utilizing the fusion procedure within affine Hecke algebra frameworks.

Contribution

It introduces a hierarchy of commutative elements satisfying generalized functional relations in open Hecke chain models, expanding the algebraic understanding of integrable systems.

Findings

Constructed a hierarchy of commutative elements using fusion.

Derived generalized functional relations for these elements.

Linked the relations to known transfer-matrix relations in solvable spin chains.

Abstract

We consider integrable open chain models formulated in terms of generators of affine Hecke algebras. The hierarchy of commutative elements (which are analogs of the commutative transfer-matrices) are constructed by using the fusion procedure. These elements satisfy a set of functional relations which generalize functional relations among a family of transfer-matrices in solvable spin chain models of U_q(gl(n|m)) type.