63 citations · 417 across the 32 of their papers we have counts for
32 papers
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…
Generalized Macdonald functions and quantum toroidal gl(1) algebra
Jean-Emile Bourgine, Luca Cassia, Artem Stoyan
The Macdonald operator is known to coincide with a certain element of the quantum toroidal algebra in the Fock representation of levels . A generalization…
A Calogero model for the non-Abelian quantum Hall effect
Jean-Emile Bourgine, Yutaka Matsuo
A model of the non-Abelian fractional quantum Hall effect is obtained from the diagonalization of the matrix model proposed by Dorey, Tong, and Turner (DTT). The Hamiltonian is rem…
A -deformation of the 2d Toda integrable hierarchy
Jean-Emile Bourgine, Alexandr Garbali
A -deformation of the 2d Toda integrable hierarchy is introduced by enhancing the underlying symmetry algebra to the quan…
Shifted quantum groups and matter multiplets in supersymmetric gauge theories
Jean-Emile Bourgine
The notion of shifted quantum groups has recently played an important role in algebraic geometry. This subtle modification of the original definition brings more flexibility in the…
Engineering 3D theories using the quantum affine algebra
Jean-Emile Bourgine
The algebraic engineering technique is applied to a class of 3D gauge theories on the omega-deformed background . The vortex partition fun…