Algebro-Geometric Solutions of the Generalized Virasoro Constraints

Symmetry Integrability and Geometry-Methods and Applications

article

Francisco José Plaza Martín¹ 

[1] Universidad de Salamanca

关键词: string equation;    Virasoro constraints;    KP hierarchy;    Gl(n)-opers;    Sato Grassmannian;    topological recursion;   

DOI  :  10.3842/SIGMA.2015.052

来源: National Academy of Science of Ukraine

【 摘 要 】

We will describe algebro-geometric solutions of the KdV hierarchy whose $\tau$-functions in addition satisfy a generalization of the Virasoro constraints (and, in particular, a generalization of the string equation). We show that these solutions are closely related to embeddings of the positive half of the Virasoro algebra into the Lie algebra of differential operators on the circle. Our results are tested against the case of Witten-Kontsevich $\tau$-function. As by-products, we exhibit certain links of our methods with double covers of the projective line equipped with a line bundle and with ${\rm Gl}(n)$-opers on the punctured disk.

【 授权许可】

Unknown