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

Abstract

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.

relation with Kazhdan-Lusztig basis added; text modified; 2 figures added

References in corpus (3)

• Sum rules for the ground states of the O(1) loop model on a cylinder and the XXZ spin chain
• Totally Symmetric Self-Complementary Plane Partitions and Quantum Knizhnik-Zamolodchikov equation: a conjecture
• Symmetric polynomials vanishing on the shifted diagonals and Macdonald polynomials

Cited by in corpus (4)

• Ground-state properties of a supersymmetric fermion chain
• Exact finite size groundstate of the O(n=1) loop model with open boundaries
• The quantum Knizhnik-Zamolodchikov equation and non-symmetric Macdonald polynomials
• A_k Generalization of the O(1) Loop Model on a Cylinder: Affine Hecke Algebra, q-KZ Equation and the Sum Rule