3 papers
math.QA2026
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…
math-ph2025
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…
math-ph2024
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…