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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…
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Asymmetric Simple Exclusion Process with Open Boundaries and Koornwinder Polynomials

In this paper, we analyze the steady state of the asymmetric simple exclusion process with open boundaries and second class particles by deforming it through the introduction of spectral parameters.…
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Inhomogenous Multispecies TASEP on a ring with spectral parameters

We study an inhomogenous multispecies version of the Totally Asymmetric Simple Exclusion Process (TASEP) on a periodic oriented one dimensional lattice, which depends on two sets of parameters $({\bf…
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Nonabelian Bundle Gerbes, Their Differential Geometry and Gauge Theory

Bundle gerbes are a higher version of line bundles, we present nonabelian bundle gerbes as a higher version of principal bundles. Connection, curving, curvature and gauge transformations are studied…
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Proof of the Razumov-Stroganov conjecture

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

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 corollary we obtain that…
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A one-parameter refinement of the Razumov-Stroganov correspondence

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Integral Formulas and Antisymmetrization Relations for the Six-Vertex Model

We study the relationship between various integral formulas for nonlocal correlation functions of the six-vertex model with domain wall boundary conditions. Specifically, we show how the known…
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Off-critical SLE(2) and SLE(4): a field theory approach

Using their relationship with the free boson and the free symplectic fermion, we study the off-critical perturbations of SLE(4) and SLE(2) obtained by adding a mass term to the action. We compute the…
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Matrix product and sum rule for Macdonald polynomials

International audience We present a new, explicit sum formula for symmetric Macdonald polynomials Pλ and show that they can be written as a trace over a product of (infinite dimensional) matrices.…
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