65 citations · 527 across the 30 of their papers we have counts for
29 papers
(1,k) CFT and RH problem with the c=-2 case
Mikhail Bershtein, Andrei Grigorev, Anton Shchechkin
Following approach of Iorgov--Lisovyy--Teschner, we construct solutions of the (modified) Riemann--Hilbert problem using conformal blocks of Virasoro models. For case…
Athinization of irreducible -modules with dominant highest weights
Mikhail Bershtein, Evgeny Mukhin, Leonid Rybnikov +1
We study the Gelfand-Tsetlin realization of generic Verma modules for the affine Lie algebra by viewing them as thin modules over the affine Yangian $Y(…
Deformed W-algebras and chiralized cluster seeds: subregular W-algebras and Inverse Quantum Hamiltonian Reduction
Mikhail Bershtein, Jean-Emile Bourgine, Ethan Fursman
The recently introduced formalism of chiral cluster seeds replaces quantum cluster variables with deformed vertex operators. In this framework, a decorated quiver associated with a…
Cluster integrable systems
Mikhail Bershtein
In these lecture notes, we give an introduction to cluster integrable systems. The topics include relativistic Toda systems, moduli spaces of framed local systems, Goncharov-Kenyon…
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…
Highest-weight vectors and three-point functions in GKO coset decomposition
Mikhail Bershtein, Boris Feigin, Aleksandr Trufanov
We revisit the classical Goddard-Kent-Olive coset construction. We find the formulas for the highest weight vectors in coset decomposition and calculate their norms. We also derive…