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 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.
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Kasatani, M., Pasquier, V. On Polynomials Interpolating Between the Stationary State of a O(n) Model and a Q.H.E. Ground State. Commun. Math. Phys. 276, 397–435 (2007). https://doi.org/10.1007/s00220-007-0341-0
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DOI: https://doi.org/10.1007/s00220-007-0341-0