On boundary fusion and functional relations in the Baxterized affine Hecke algebra

TL;DR

This paper develops boundary operators in the Baxterized affine Hecke algebra, leading to new commuting transfer matrices and fusion relations, advancing the algebraic understanding of integrable models with boundaries.

Contribution

It introduces boundary operators satisfying fused reflection equations for arbitrary representations, extending the algebraic framework of integrable models with boundaries.

Findings

Constructed boundary operators satisfying fused reflection equations.

Established a family of commuting transfer matrices of Sklyanin type.

Derived fusion functional relations for specific representations.

Abstract

We construct boundary type operators satisfying fused reflection equation for arbitrary representations of the Baxterized affine Hecke algebra. These operators are analogues of the fused reflection matrices in solvable half-line spin chain models. We show that these operators lead to a family of commuting transfer matrices of Sklyanin type. We derive fusion type functional relations for these operators for two families of representations.