Quasi-polynomial extensions of nonsymmetric Macdonald-Koornwinder polynomials

Abstract: In a recent preprint the author with Sahi and Venkateswaran introduced families of actions of the double affine Hecke algebra on spaces of quasi-polynomials. These so-called quasi-polynomial representations led to the introduction of quasi-polynomial extensions of the nonsymmetric Macdonald polynomials which reduce to metaplectic Iwahori-Whittaker functions in the $\mathfrak{p}$-adic limit. In this paper we extend the quasi-polynomial representations to Sahi's 5-parameter double affine Hecke algebra and introduce the quasi-polynomial extensions of the nonsymmetric Koornwinder polynomials.