Sklyanin Determinant for Reflection Algebra

TL;DR

This paper provides a combinatorial framework for computing the Sklyanin determinant, which is crucial for understanding the center of reflection algebras associated with integrable models with boundaries.

Contribution

It introduces a combinatorial description of the Sklyanin determinant, enabling explicit calculations and advancing the algebraic understanding of reflection algebras.

Findings

Combinatorial description of Sklyanin determinant provided

Facilitates explicit computations in reflection algebras

Enhances understanding of the algebraic structure of integrable models

Abstract

Reflection algebras is a class of algebras associated with integrable models with boundaries. The coefficients of Sklyanin determinant generate the center of the reflection algebra. We give a combinatorial description of Sklyanin determinant suitable for explicit computations.