Algebro-Geometric Solutions of the Generalized Virasoro Constraints

作者：Plaza Martin Francisco Jose

来源：Symmetry Integrability and Geometry-Methods and Applications, 2015, 11: 052.

DOI：10.3842/SIGMA.2015.052

• string equation
• Virasoro constraints
• KP hierarchy
• Gl(n)-opers
• Sato Grassmannian
• topological recursion

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 Gl(n)-opers on the punctured disk.

• 出版日期2015