Analytic Bethe ansatz related to a one parameter family of finite dimensional representations of the Lie superalgebra sl(r+1|s+1)

TL;DR

This paper develops an analytic Bethe ansatz for a family of finite-dimensional representations of the Lie superalgebra sl(r+1|s+1), providing new determinant formulae and transfer matrix eigenvalues depending on a continuous parameter.

Contribution

It introduces deformed determinant formulae for transfer matrices related to a one-parameter family of representations of sl(r+1|s+1), extending previous results.

Findings

Derived new formulae for transfer matrix eigenvalues.

Connected solutions to a graded Yang-Baxter equation.

Identified functional relations among transfer matrices.

Abstract

As is well known, the type 1 Lie superalgebra sl(r+1|s+1) admits a one parameter family of finite dimensional irreducible representations. We have carried out an analytic Bethe ansatz related to this family of representations. We present formulae, which are deformations of previously proposed determinant formulae labeled by a Young superdiagram. These formulae will provide transfer matrix eigenvalues in dressed vacuum form related to the solutions of a graded Yang-Baxter equation, which depend not only on the spectral parameter but also on a non-additive continuous parameter. A class of transfer matrix functional relations among these formulae is briefly mentioned.