Alexandr Garbali

activity

20182025

collaborators

3 papers

math.QA2025

Shuffle algebras, lattice paths and quantum toroidal $gl_{n ∣ m}$

Alexandr Garbali, Andrei Neguţ

We describe and compute various families of commuting elements of the matrix shuffle algebra of type $gl_{n ∣ m}$ , which is expected to be isomorphic to quantum toroidal $…

math.CO2024

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 $F_{S}$ and $G_{S}$ ; these are in direct analogy with fu…

math.CO2018

Modified Macdonald polynomials and integrability

Alexandr Garbali, Michael Wheeler

We derive combinatorial formulae for the modified Macdonald polynomial $H_{λ} (x; q, t)$ using coloured paths on a square lattice with quasi-cylindrical boundary conditions. The derivat…

Shuffle algebras, lattice paths and quantum toroidal gln∣m​

Rational symmetric functions from the Izergin-Korepin 19-vertex model

Modified Macdonald polynomials and integrability

Shuffle algebras, lattice paths and quantum toroidal $gl_{n ∣ m}$