# Analytic Bethe ansatz and functional relations related to tensor-like representations of type II Lie superalgebras B(r|s) and D(r|s)

## TL;DR

This paper develops an analytic Bethe ansatz for tensor-like representations of certain Lie superalgebras, providing eigenvalue formulas and functional relations for transfer matrices, including a complete set for the B(0|s) case.

## Contribution

It introduces new eigenvalue formulas and functional relations for transfer matrices associated with tensor-like representations of type II Lie superalgebras B(r|s) and D(r|s).

## Key findings

- Eigenvalue formulas for transfer matrices in dressed vacuum forms.
- Functional relations (T-system) for these transfer matrices.
- Complete set of relations for B(0|s)=osp(1|2s) case.

## Abstract

An analytic Bethe ansatz is carried out related to tensor-like representations of the type II Lie superalgebras B(r|s)=osp(2r+1|2s) (r > -1, s >0) and D(r|s)=osp(2r|2s) (r >1, s >0). We present eigenvalue formulae of transfer matrices in dressed vacuum forms labeled by Young (super) diagrams. A class of transfer matrix functional relations (T-system) is discussed. In particular for B(0|s)=osp(1|2s)(s >0) case, a complete set of functional relations is proposed by using duality among dressed vacuum forms.

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Source: https://tomesphere.com/paper/0911.5393