On Polynomials Interpolating Between the Stationary State of a <Emphasis Type="Italic">O</Emphasis>(<Emphasis Type="Italic">n</Emphasis>) Model and a Q.H.E. Ground State

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 positive in n. At n = 1, they coincide with 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.