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Coloured stochastic vertex models and their spectral theory

- A. Borodin, M. Wheeler
- Mathematics, Physics
- 6 August 2018

This work is dedicated to $\mathfrak{sl}_{n+1}$-related integrable stochastic vertex models; we call such models coloured. We prove several results about these models, which include the following: … Expand

Shift‐invariance for vertex models and polymers

- A. Borodin, V. Gorin, M. Wheeler
- Mathematics, PhysicsProceedings of the London Mathematical Society
- 6 December 2019

We establish a symmetry in a variety of integrable stochastic systems: Certain multi-point distributions of natural observables are unchanged under a shift of a subset of observation points. The… Expand

Matrix product formula for Macdonald polynomials

- L. Cantini, J. Gier, M. Wheeler
- Mathematics, Physics
- 1 May 2015

We derive a matrix product formula for symmetric Macdonald polynomials. Our results are obtained by constructing polynomial solutions of deformed Knizhnik--Zamolodchikov equations, which arise by… Expand

A New Generalisation of Macdonald Polynomials

- A. Garbali, J. Gier, M. Wheeler
- Mathematics, Physics
- 23 May 2016

We introduce a new family of symmetric multivariate polynomials, whose coefficients are meromorphic functions of two parameters (q, t) and polynomial in a further two parameters (u, v). We evaluate… Expand

Nonsymmetric Macdonald polynomials via integrable vertex models

- A. Borodin, M. Wheeler
- Mathematics, Physics
- 15 April 2019

Starting from an integrable rank-$n$ vertex model, we construct an explicit family of partition functions indexed by compositions $\mu = (\mu_1,\dots,\mu_n)$. Using the Yang-Baxter algebra of the… Expand

Colored Fermionic Vertex Models and Symmetric Functions

- A. Aggarwal, A. Borodin, M. Wheeler
- Mathematics, Physics
- 5 January 2021

In this text we introduce and analyze families of symmetric functions arising as partition functions for colored fermionic vertex models associated with the quantized affine Lie superalgebra Uq (… Expand

Refined Cauchy/Littlewood identities and six-vertex model partition functions: III. Deformed bosons

- M. Wheeler, P. Zinn-Justin
- Mathematics, Physics
- 10 August 2015

Refined Cauchy/Littlewood identities and six-vertex model partition functions: II. Proofs and new conjectures

- D. Betea, M. Wheeler, P. Zinn-Justin
- Mathematics, Physics
- 27 May 2014

We prove two identities of Hall–Littlewood polynomials, which appeared recently in Betea and Wheeler (2014). We also conjecture, and in some cases prove, new identities which relate infinite sums of… Expand

Between the stochastic six vertex model and Hall-Littlewood processes

- A. Borodin, Alexey Bufetov, M. Wheeler
- Mathematics, Physics
- 29 November 2016

We prove that the joint distribution of the values of the height function for the stochastic six vertex model in a quadrant along a down-right path coincides with that for the lengths of the first… Expand

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