On quantum $\mathfrak{osp}(1|2\ell)$-Toda chain

TL;DR

This paper explores the quantum $rak{osp}(1|2 ext{-} ext{ell})$-Toda chain, revealing its equivalence to a $BC_ ext{ell}$-Toda chain and discussing the underlying reasons for this connection.

Contribution

It establishes a link between the $rak{osp}(1|2 ext{-} ext{ell})$-Toda chain and the $BC_ ext{ell}$-Toda chain, providing insights into their relationship within super Lie algebra frameworks.

Findings

The $rak{osp}(1|2 ext{-} ext{ell})$-Toda chain is equivalent to a $BC_ ext{ell}$-Toda chain.

The paper discusses the reasons behind this equivalence.

It advances understanding of super Lie algebra related integrable systems.

Abstract

The orthosymplectic super Lie algebra $\mathfrak{osp}(1|\,2\ell)$ is the closest analog of standard Lie algebras in the world of super Lie algebras. We demonstrate that the corresponding $\mathfrak{osp}(1|\,2\ell)$-Toda chain turns out to be an instance of a $BC_\ell$-Toda chain. The underlying reason for this relation is discussed.