Simple Construction of Elliptic Boundary K-Matrix

TL;DR

This paper constructs an elliptic K-matrix satisfying the boundary Yang-Baxter equation by deriving an infinite-dimensional representation and then restricting it to finite dimensions, linked to Belavin's R-matrix.

Contribution

It provides a new explicit construction of elliptic K-matrices associated with Belavin's R-matrix, advancing boundary integrable models.

Findings

Derived infinite-dimensional representation of elliptic K-operator.

Constructed finite-dimensional elliptic K-matrix from the representation.

Connected the K-matrix construction to Belavin's R-matrix.

Abstract

We give the infinite-dimensional representation for the elliptic $ K $-operator satisfying the boundary Yang-Baxter equation. By restricting the functional space to finite-dimensional space, we construct the elliptic $ K $-matrix associated to Belavin's completely $ \mathbb{Z} $-symmetric $ R $-matrix.