49 citations · 147 across the 8 of their papers we have counts for
8 papers
Cluster Reductions, Mutations, and -Painlevé Equations
Mikhail Bershtein, Pavlo Gavrylenko, Andrei Marshakov +1
We propose an extension of the Goncharov-Kenyon class of cluster integrable systems by their Hamiltonian reductions. This extension allows us to fill in the gap in cluster construc…
Cluster Toda chains and Nekrasov functions
M. Bershtein, P. Gavrylenko, A. Marshakov
In this paper the relation between the cluster integrable systems and -difference equations is extended beyond the Painlevé case. We consider the class of hyperelliptic curves w…
Cluster integrable systems, q-Painleve equations and their quantization
M. Bershtein, P. Gavrylenko, A. Marshakov
We discuss the relation between the cluster integrable systems and -difference Painlevé equations. The Newton polygons corresponding to these integrable systems are all 16 conve…
Twist-field representations of W-algebras, exact conformal blocks and character identities
M. Bershtein, P. Gavrylenko, A. Marshakov
We study the twist-field representations of W-algebras and generalize construction of the corresponding vertex operators to D- and B-series. It is shown, how the computation of cha…
Free fermions, W-algebras and isomonodromic deformations
P. Gavrylenko, A. Marshakov
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.…
Exact conformal blocks for the W-algebras, twist fields and isomonodromic deformations
P. Gavrylenko, A. Marshakov
We consider the conformal blocks in the theories with extended conformal W-symmetry for the integer Virasoro central charges. We show that these blocks for the generalized twist fi…
Isomonodromic -functions and conformal blocks
P. Gavrylenko
We study the solution of the Schlesinger system for the 4-point isomonodromy problem and conjecture an expression for the isomonodromic -function in terms of 2…
Residue Formulas for Prepotentials, Instanton Expansions and Conformal Blocks
P. Gavrylenko, A. Marshakov
We study the extended prepotentials for the S-duality class of quiver gauge theories, considering them as quasiclassical tau-functions, depending on gauge theory condensates and ba…