John HARNAD, Universit茅 Concordia et CRM
John HARNAD, Universit茅 Concordia et CRM
Seminar Physique Math茅matique
CRM, UdeM, Pavillon Andr茅-Aisenstadt, 2920, ch. de la Tour, salle 4336
The fermionic construction of $tau$-functions of the KP hierarchy is extended to the construction of bases adapted to the choice of the element W of the infinite Grassmannian corresponding to the initial conditions of the KP flows, as well as to the multi-pair and multicurrent correlators. The latter serve as alternative generating functions for the enumerative invariants associated to particular choices of W, with their genus expansion coefficients satisfying the topological recursion relations. The choice of W that gives rise to generating functions for infinite parametric families of weighted Hurwitz numbers corresponds to $ au$-functions of hypergeometric type. The Kac-Schwarz operators leaving the subspace W invariant are shown to lead to the associated quantum spectral curve.