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Thermodynamic limit of the six-vertex model with domain wall boundary conditions
We address the question of the dependence of the bulk free energy on boundary conditions for the six-vertex model. Here we compare the bulk free energy for periodic and domain wall boundary
On some integrals over the U(N) unitary group and their large N limit
The integral over the U(N) unitary group I = ? DU exp Tr AU BU? is re-examined. Various approaches and extensions are first reviewed. The second half of the paper deals with more recent developments:
Around the Razumov-Stroganov Conjecture: Proof of a Multi-Parameter Sum Rule
We prove that the sum of entries of the suitably normalized groundstate vector of the $O(1)$ loop model with periodic boundary conditions on a periodic strip of size $2n$ is equal to the total number
Jucys–Murphy Elements and Weingarten Matrices
We provide a compact proof of the recent formula of Collins and Matsumoto for the Weingarten matrix of the orthogonal group using Jucys–Murphy elements.
Loop model with mixed boundary conditions, qKZ equation and alternating sign matrices
The integrable loop model with mixed boundary conditions based on the 1-boundary extended Temperley–Lieb algebra with loop weight 1 is considered. The corresponding qKZ equation is introduced and its
Littlewood-Richardson Coefficients and Integrable Tilings
TLDR
This work provides direct proofs of product and coproduct formulae for Schur functions where the coefficients (Littlewood--Richardson coefficients) are defined as counting puzzles based on the quantum integrability of the underlying tiling model.
Six-vertex, Loop and Tiling Models: Integrability and Combinatorics
This is a review (including some background material) of the author's work and related activity on certain exactly solvable statistical models in two dimensions, including the six-vertex model, loop
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