Additional Symmetry of CKP hierarchy

TL;DR

This paper explores the additional symmetries and algebraic structures of the CKP hierarchy, revealing a new infinite-dimensional algebra and deriving higher order constraints and properties.

Contribution

It introduces the $W^C_{1+ abla}$ algebra as a subalgebra of $W_{1+ abla}$ and establishes new symmetry flows and constraints for the CKP hierarchy.

Findings

Additional symmetry flows form a new algebra $W^C_{1+ abla}$

Higher order constraints on $L^l$ are derived

Properties of the generating function are analyzed

Abstract

Based on the Orlov and Shulman's M operator, the additional symmetries and the string equation of the CKP hierarchy are established, and then the higher order constraints on $L^l$ are obtained. In addition, the generating function and some properties are also given. In particular, the additional symmetry flows form a new infinite dimensional algebra $W^C_{1+\infty}$, which is a subalgebra of $W_{1+\infty}$.