Additional Symmetry of CKP hierarchy

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 $W_{1+\mathrm{\infty }}^C$, which is a subalgebra of $W_{1+\mathrm{\infty }}$.