Free fermions, W-algebras and isomonodromic deformations

Understand

We consider the theory of multicomponent free massless fermions in two dimensions and use it for construction of representations of W-algebras at integer Virasoro central charges.

• We define the vertex operators in this theory in terms of solutions of the corresponding isomonodromy problem.
• We use this construction to get some new insights on tau-functions of the multicomponent Toda type hierarchies for the class of solutions, given by the isomonodromy vertex operators and get useful representation for the tau-function of isomonodromic deformations.