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This article is cited in 5 scientific papers (total in 5 papers)
Algebro-Geometric Solutions of the Generalized Virasoro Constraints
Francisco José Plaza Martín Departamento de Matemáticas and IUFFYM, Universidad de Salamanca, Plaza de la Merced 1-4, 37008 Salamanca, Spain
Abstract:
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 $\mathrm{Gl}(n)$-opers on the punctured disk.
Keywords:
string equation; Virasoro constraints; KP hierarchy; $\mathrm{Gl}(n)$-opers; Sato Grassmannian; topological recursion.
Received: December 20, 2014; in final form July 2, 2015; Published online July 7, 2015
Citation:
Francisco José Plaza Martín, “Algebro-Geometric Solutions of the Generalized Virasoro Constraints”, SIGMA, 11 (2015), 052, 34 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1033 https://www.mathnet.ru/eng/sigma/v11/p52
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