24 citations · 53 across the 11 of their papers we have counts for
13 papers
Positivity of the basic hypergeometric series and the MacMahon identity
Alexandr Garbali
The basic hypergeometric series whose upper and lower parameters are non-negative integer powers of satisfying a certain constraint can be, after a normalisatio…
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…
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…
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…
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…
Shuffle algebras, lattice paths and the commuting scheme
Alexandr Garbali, Paul Zinn-Justin
The commutative trigonometric shuffle algebra is a space of symmetric rational functions satisfying certain wheel conditions. We describe a ring isomorphism between $…
The -matrix of the quantum toroidal algebra in the Fock module
Alexandr Garbali, Jan de Gier
We propose a method to compute the -matrix on a tensor product of Fock modules from coproduct relations in a Hopf algebra. We apply this method to the quantum toroidal algeb…
Modified Macdonald polynomials and integrability
Alexandr Garbali, Michael Wheeler
We derive combinatorial formulae for the modified Macdonald polynomial using coloured paths on a square lattice with quasi-cylindrical boundary conditions. The derivat…
A curious mapping between supersymmetric quantum chains
Gyorgy Z. Feher, Alexandr Garbali, Jan de Gier +1
We present a unitary transformation relating two apparently different supersymmetric lattice models in one dimension. The first \cite{FS07} describes semionic particles on a 1D lad…
Koornwinder polynomials and the stationary multi-species asymmetric exclusion process with open boundaries
Luigi Cantini, Alexandr Garbali, Jan de Gier +1
We prove that the normalisation of the stationary state of the multi-species asymmetric simple exclusion process (mASEP) is a specialisation of a Koornwinder polynomial. As a corol…
A new generalisation of Macdonald polynomials
Alexandr Garbali, Jan de Gier, Michael Wheeler
We introduce a new family of symmetric multivariate polynomials, whose coefficients are meromorphic functions of two parameters and polynomial in a further two parameters $…