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

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Cited by in corpus (19)

• Matrix product formula for Macdonald polynomials
• Spin chains with dynamical lattice supersymmetry
• Spin-Singlet Quantum Hall States and Jack Polynomials with a Prescribed Symmetry
• Ground-state properties of a supersymmetric fermion chain
• Jack polynomial fractional quantum Hall states and their generalizations
• Exact finite size groundstate of the O(n=1) loop model with open boundaries
• Mapping the Calogero model on the Anyon model
• Spin-Ruijsenaars, q-deformed Haldane-Shastry and Macdonald polynomials
• Factorised solutions of Temperley-Lieb $q$KZ equations on a segment
• The quantum Knizhnik-Zamolodchikov equation and non-symmetric Macdonald polynomials
• Spinless basis for spin-singlet FQH states
• A_k Generalization of the O(1) Loop Model on a Cylinder: Affine Hecke Algebra, q-KZ Equation and the Sum Rule
• Fusion rules and structure constants of E-series minimal models
• Currents in the dilute $O(n=1)$ model
• Graphical Calculus for the Double Affine Q-Dependent Braid Group
• Finite size lattice results for the two-boundary Temperley--Lieb loop model
• Towers of solutions of qKZ equations and their applications to loop models
• Laurent polynomial solutions of the boundary quantum Knizhnik--Zamolodchikov equation
• Quantum affine Knizhnik-Zamolodchikov equations and quantum spherical functions, I