On $W_{1+\infty}$ $n$-algebra

TL;DR

This paper introduces a novel $W_{1+ abla}$ $n$-algebra, explores its properties in quantum Landau systems, and discusses implications for many-body physics and vertex operator correlations.

Contribution

It presents the first detailed analysis of the $W_{1+ abla}$ $n$-algebra and its realization in Landau problems and many-body systems.

Findings

Properties of the $W_{1+ abla}$ $n$-algebra are characterized.

Realization of the classical $w_{ abla}$ 3-algebra is demonstrated.

Constraints for correlation functions in many-body Landau systems are derived.

Abstract

We present the nontrivial $W_{1+\infty}$ $n$-algebra and analyze its remarkable properties. We investigate the $W_{1+\infty}$ $n$-algebra in the Landau problem and discuss the realization of the classical $w_{\infty}$ 3-algebra. Furthermore, we discuss the case of the many-body system in the lowest Landau level and derive the constraints for correlation functions of the vertex operators.