3-Algebraic structures of the quantum Calogero-Moser model

TL;DR

This paper explores the quantum Calogero-Moser model's hidden symmetries, revealing its underlying $W_{1+ abla}$ and Virasoro-Witt 3-algebras, and their reductions in the large N limit to simpler algebraic structures.

Contribution

It uncovers the hidden 3-algebraic symmetries of the quantum Calogero-Moser model and analyzes their behavior in the large N limit.

Findings

Identification of $W_{1+ abla}$ and Virasoro-Witt 3-algebras as symmetries

Reduction to $w_{ abla}$ and special Virasoro-Witt 3-algebras in large N limit

Both reduced algebras satisfy the fundamental identity

Abstract

We investigate the quantum Calogero-Moser model and reveal its hidden symmetries, i.e., the $W_{1+\infty}$ and Virasoro-Witt 3-algebras. In the large $N$ limit, we note that these two infinite dimensional 3-algebras reduce to the $w_{\infty}$ and special Virasoro-Witt 3-algebras which satisfy the fundamental identity condition, respectively.