Virasoro type algebraic structure hidden in the constrained discrete KP hierarchy

TL;DR

This paper reveals that the symmetry flows of the constrained discrete KP hierarchy form a Virasoro algebra, uncovering a deep algebraic structure in integrable systems.

Contribution

It constructs the additional symmetries of the constrained discrete KP hierarchy and proves their algebraic structure as the positive half of the Virasoro algebra.

Findings

Symmetry flows form a Virasoro algebra

Constructed additional symmetries for the cdKP hierarchy

Established algebraic structure of symmetries

Abstract

In this paper, we construct the additional symmetries of one-component constrained discrete KP (cdKP) hierarchy, and then prove that the algebraic structure of the symmetry flows is the positive half of Virasoro algebra.