6 papers
Shuffle algebras, lattice paths and quantum toroidal
Alexandr Garbali, Andrei Neguţ
We describe and compute various families of commuting elements of the matrix shuffle algebra of type , which is expected to be isomorphic to quantum toroidal $…
Learning the symmetric group: large from small
Max Petschack, Alexandr Garbali, Jan de Gier
Machine learning explorations can make significant inroads into solving difficult problems in pure mathematics. One advantage of this approach is that mathematical datasets do not…
Rational symmetric functions from the Izergin-Korepin 19-vertex model
Alexandr Garbali, Weiying Guo, Michael Wheeler
Starting from the Izergin-Korepin 19-vertex model in the quadrant, we introduce two families of rational multivariate functions and ; these are in direct analogy with fu…
Shuffle algebras, lattice paths and Macdonald functions
Alexandr Garbali, Ajeeth Gunna
We consider partition functions on the square lattice with the local Boltzmann weights given by the -matrix of the quantum algebra. We i…
Symmetric functions from the six-vertex model in half-space
Alexandr Garbali, Jan de Gier, William Mead +1
We study the stochastic six-vertex model in half-space with generic integrable boundary weights, and define two families of multivariate rational symmetric functions. Using commuta…
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…