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Coloured stochastic vertex models and their spectral theory
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:
Shift‐invariance for vertex models and polymers
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
Spin q–Whittaker polynomials
Matrix product formula for Macdonald polynomials
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
A New Generalisation of Macdonald Polynomials
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
Nonsymmetric Macdonald polynomials via integrable vertex models
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
Colored Fermionic Vertex Models and Symmetric Functions
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 (
Refined Cauchy/Littlewood identities and six-vertex model partition functions: II. Proofs and new conjectures
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
Between the stochastic six vertex model and Hall-Littlewood processes
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