Abstract

We propose new conjectures relating sum rules for the polynomial solution of the qKZequation with open (reflecting) boundaries as a function of the quantum parameterq andthe τ-enumeration of plane partitions with specific symmetries, withτ = −(q+q−1). We also find a conjectural relation à la Razumov–Stroganov between the limit of the qKZ solution and refined numbers of totally symmetric self-complementaryplane partitions.

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