Quantum Torus symmetries of the CKP and multi-component CKP hierarchies

TL;DR

This paper constructs quantum Torus symmetries for the CKP and multi-component CKP hierarchies, revealing a rich algebraic structure that extends known symmetries in integrable systems.

Contribution

It introduces a new quantum Torus symmetry framework for CKP hierarchies, expanding the understanding of their algebraic structures.

Findings

Constructed additional flows forming a quantum Torus symmetry

Demonstrated algebraic structure with double indices

Compared with $W_{0}$ symmetry, highlighting differences

Abstract

In this paper, we construct a series of additional flows of the CKP hierarchy and the multi-component CKP hierarchy and these flows constitute a N-folds direct product of the positive half of the quantum Torus symmetry. Comparing to the $W_{\infty}$ infinite dimensional Lie symmetry, this quantum Torus symmetry has a nice algebraic structure with double indices.