Negative Generators of the Virasoro Constraints for the BKP Hierarchy

Abstract

We give a straightforward derivation of the string equation and Virasoro constraints on the $\tau$ function of the BKP hierarchy by means of some special additional symmetry flows. The explicit forms of the actions of these additional symmetry flows on the wave function and then the negative Virasoro generators $L_{-k}$ are given, where $k$ is a positive integer.

arXiv comment11 pages by AMS latex style; To appear in Chinese Quarterly Journal of Mathematics 24(2009)

References in corpus (5)

• Integrability and Matrix Models
• On additional symmetries of the KP hierarchy and Sato's Bäcklund transformation
• On the BKP hierarchy: additional symmetries, Fay identity and Adler-Shiota-van Moerbeke formula
• Additional symmetries of KP, Grassmannian, and the string equation
• The $n$--TH Reduced BKP Hierarchy, the String Equation and $B{W}_{1+\infty }$--Constraints