On polynomials interpolating between the stationary state of a O(n) model and a Q.H.E. ground state

M. Kasatani, V. Pasquier

Published 2006-08-07, updated 2007-04-09Version 3

We obtain a family of polynomials defined by vanishing conditions and associated to tangles. We study more specifically the case where they are related to a O(n) loop model. We conjecture that their specializations at $z_i=1$ are {\it positive} in $n$. At $n=1$, they coincide with the the Razumov-Stroganov integers counting alternating sign matrices. We derive the CFT modular invariant partition functions labelled by Coxeter-Dynkin diagrams using the representation theory of the affine Hecke algebras.