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Proof of the Razumov-Stroganov conjecture
The Razumov-Stroganov conjecture relates the ground-state coefficients in the periodic even-length dense O(1) loop model to the enumeration of fully-packed loop configurations on the square, withExpand
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.Expand
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 studiedExpand
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 $({\bfExpand
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 byExpand
Algebraic Bethe ansatz for the two species ASEP with different hopping rates
An ASEP with two species of particles and different hopping rates is considered on a ring. Its integrability is proved, and the nested algebraic Bethe ansatz is used to derive the Bethe equations forExpand
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 thatExpand
A one-parameter refinement of the Razumov-Stroganov correspondence
A one-parameter refinement of the Razumov-Stroganov correspondence is introduced and proved for fully-packed loop configurations (FPL) on domains which generalize the square domain, and which are endowed with the gyration operation. Expand
qKZ equation and ground state of the O(1) loop model with open boundary conditions
We consider the qKZ equations based on the two boundaries Temperley Lieb algebra. We construct their solution in the case s = q −3/2 using a recursion relation. At the combinatorial point q 1/2 = eExpand
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 theExpand