Diagonalization of transfer matrix of supersymmetry $u_q(\hat{sl}(m+1|n+1))$ chain with a boundary

TL;DR

This paper analyzes the supersymmetric quantum affine algebra model with boundary conditions, diagonalizing its transfer matrix using bosonization techniques, advancing understanding of integrable supersymmetric systems.

Contribution

It introduces a method to diagonalize the transfer matrix of a boundary supersymmetric quantum affine algebra model using bosonization.

Findings

Successful diagonalization of the transfer matrix.

Extension of algebraic analysis to boundary supersymmetric models.

Enhanced understanding of supersymmetric integrable systems.

Abstract

We study the supersymmetry $U_q(\hat{sl}(M+1|N+1))$ analogue of the supersymmetric t-J model with a boundary, in the framework of the algebraic analysis method. We diagonalize the commuting transfer matrix by using the bosonization of the vertex operator associated with the quantum affine supersymmetry.