Lattice Analogue of W-infinity Algebra and Discrete KP-Hierarchy

TL;DR

This paper introduces a lattice version of the $W_{}$-algebra linked to integrable systems, explores reductions to lattice $W_N$-algebras, and connects these findings with existing research on discrete hierarchies.

Contribution

It defines the lattice $W_{}$-algebra and describes its reductions, advancing the understanding of lattice analogues of $W$-algebras and their relation to discrete integrable hierarchies.

Findings

Defined lattice $W_{}$-algebra for integrable systems.

Described reductions to lattice $W_N$-algebras.

Connected results with existing studies on discrete hierarchies.

Abstract

In development of the started activity on lattice analogues of $W$-algebras, we define the notion of lattice $W_{\infty}$-algebra, accociated with lattice integrable system with infinite set of fields. Various kinds of reduction to lattice $W_N$-algebras, related to discrete $N$-KdV hierarchies are described. We also discuss the connection of our results with those obtained in the papers of Xiong [13] and Bonora [14].