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… Expand

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:… Expand

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… Expand

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.

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… Expand

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.Expand

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… Expand