Sasha Garbali

Computing the R-matrix of the quantum toroidal algebra

Alexandr Garbali, Andrei Negut

Journal article  |  2023  |  JOURNAL OF MATHEMATICAL PHYSICS

We consider the problem of the R-matrix of the quantum toroidal algebra Uq,t(gl..1) in the Fock representation. Using the connecti..

Shuffle algebras, lattice paths and the commuting scheme

A Garbali, P Zinn-Justin

Book Chapter  |  2022  |  Contemporary Mathematics

The commutative trigonometric shuffle algebra A is a space of symmetric rational functions satisfying certain wheel conditions. We..

The R-Matrix of the Quantum Toroidal Algebra Uq,t((sic)l(1)) in the Fock Module

Alexandr Garbali, Jan de Gier

Journal article  |  2021  |  COMMUNICATIONS IN MATHEMATICAL PHYSICS

We propose a method to compute the R-matrix R on a tensor product of Fock modules from coproduct relations in a Hopf algebra. We a..

Modified Macdonald Polynomials and Integrability

Alexandr Garbali, Michael Wheeler

Journal article  |  2020  |  COMMUNICATIONS IN MATHEMATICAL PHYSICS

We derive combinatorial formulae for the modified Macdonald polynomial Hλ(x; q, t) using coloured paths on a square lattice with q..

A Curious Mapping Between Supersymmetric Quantum Chains

Gyorgy Z Feher, Alexandr Garbali, Jan de Gier, Kareljan Schoutens

Book Chapter  |  2019

We present a unitary transformation relating two apparently different supersymmetric lattice models in one dimension. The first (F..

A New Generalisation of Macdonald Polynomials

Alexandr Garbali, Jan de Gier, Michael Wheeler

Journal article  |  2017  |  Communications in Mathematical Physics

We introduce a new family of symmetric multivariate polynomials, whose coefficients are meromorphic functions of two parameters (q..

The dilute Temperley-Lieb O(n=1) loop model on a semi infinite strip: the sum rule

A Garbali, B Nienhuis

Journal article  |  2017  |  JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT

This is the second part of our study of the ground state eigenvector of the transfer matrix of the dilute Temperley-Lieb loop mode..

The dilute Temperley-Lieb O(n=1) loop model on a semi infinite strip: the ground state

A Garbali, B Nienhuis

Journal article  |  2017  |  JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT

We consider the integrable dilute Temperley-Lieb (dTL) O(n = 1) loop model on a semi-infinite strip of finite width L. In the anal..

Koornwinder polynomials and the stationary multi-species asymmetric exclusion process with open boundaries

Luigi Cantini, Alexandr Garbali, Jan de Gier, Michael Wheeler

Journal article  |  2016  |  JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

We prove that the normalisation of the stationary state of the multi-species asymmetric simple exclusion process (mASEP) is a spec..

The domain wall partition function for the Izergin-Korepin nineteen-vertex model at a root of unity

A Garbali

Journal article  |  2016  |  JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT

We study the domain wall partition function Z N for the (Izergin-Korepin) integrable nineteen-vertex model on a square lattice of ..