Analytic Bethe ansatz related to the Lie superalgebra C(s)

TL;DR

This paper develops an analytic Bethe ansatz for the Lie superalgebra C(s), providing eigenvalue formulas for transfer matrices and exploring their functional relations, advancing understanding of integrable models related to superalgebras.

Contribution

It introduces eigenvalue formulas in dressed vacuum form for C(s) superalgebra transfer matrices and proposes a new DVF linked to a family of finite-dimensional irreducible representations.

Findings

Eigenvalue formulas for transfer matrices in DVF form

Functional relations among transfer matrices

Proposal of a DVF for a family of irreducible representations

Abstract

An analytic Bethe ansatz is carried out related to the type 1 Lie superalgebra C(s). We present eigenvalue formulae of transfer matrices in dressed vacuum form (DVF) labeled by Young superdiagrams with one row or one column. We also propose an DVF related to a one parameter family of finite dimensional irreducible representations. A class of transfer matrix functional relations among these formulae is discussed.