ar X iv : m at h - ph / 0 10 10 36 v 1 3 1 Ja n 20 01 Six - Vertex Model with Domain wall boundary conditions . Variable inhomogeneities

ar X iv : m at h / 06 01 74 3 v 1 [ m at h . SP ] 3 0 Ja n 20 06 DETERMINANTS OF ZEROTH ORDER OPERATORS

Six -vertex Model with Domain Wall Boundary Conditions. Variable Inhomogeneities

We consider the six-vertex model with domain wall boundary conditions. We choose the inhomogeneities as solutions of the Bethe Ansatz equations. The Bethe Ansatz equations have many solutions, so we can consider a wide variety of inho-mogeneities. For certain choices of the inhomogeneities we study arrow correlation functions on the horizontal line going through the centre. In particular we obt...

ar X iv : 0 80 6 . 01 70 v 3 [ m at h . Q A ] 1 9 Ja n 20 09 WEIGHT MULTIPLICITY POLYNOMIALS OF MULTI - VARIABLE WEYL MODULES

This paper is based on the observation that dimension of weight spaces of multi-variable Weyl modules depends polynomially on the highest weight (Conjecture 1). We support this conjecture by various explicit answers for up to three variable cases and discuss the underlying combinatorics.

ar X iv : m at h - ph / 0 30 10 19 v 1 1 5 Ja n 20 03 Which distributions of matter diffract ? — Some answers

ar X iv : 0 80 3 . 26 97 v 1 [ m at h - ph ] 1 8 M ar 2 00 8 The limit shape of large alternating sign matrices

The problem of the limit shape of large alternating sign matrices (ASMs) is addressed by studying the emptiness formation probability (EFP) in the domain-wall six-vertex model. Assuming that the limit shape arises in correspondence to the 'condensation' of almost all solutions of the saddle-point equations for certain multiple integral representation for EFP, the limit shape of large ASMs is fo...