DAHAs of Type C Cn and Character Varieties
Abstract
This paper studies the spherical subalgebra of the double affine Hecke algebra of type C Cn and relates it, at the classical level q = 1, to a certain character variety of the four-punctured Riemann sphere. This establishes a conjecture from math.QA/0504089. As a by-product, we find a completed phase space for the trigonometric van Diejen system, explicitly integrate its dynamics and explain how it can be obtained via Hamiltonian reduction.
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