Algebro-Geometric Solutions of the Generalized Virasoro Constraints

[EN]We will describe algebro-geometric solutions of the KdV hierarchy whose τ-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...

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Detalles Bibliográficos
Autor: Plaza Martín, Francisco José
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2015
País:España
Institución:Universidad de Salamanca (USAL)
Repositorio:GREDOS. Repositorio Institucional de la Universidad de Salamanca
OAI Identifier:oai:gredos.usal.es:10366/159322
Acceso en línea:http://hdl.handle.net/10366/159322
Access Level:acceso abierto
Palabra clave:string equation
Virasoro constraints
KP hierarchy
Gl(n)-opers
Sato Grassmannian
Descripción
Sumario:[EN]We will describe algebro-geometric solutions of the KdV hierarchy whose τ-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 τ-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.