Daniel Orr

Specializations of nonsymmetric Macdonald–Koornwinder polynomials

The purpose of this article is to work out the details of the Ram–Yip formula for nonsymmetric Macdonald–Koornwinder polynomials for the double affine Hecke algebras of not-necessarily reduced affine root systems. It is shown that the

Nonsymmetric difference Whittaker functions

t\rightarrow 0

The free rider and labor law: Introduction and overview

t→0 equal-parameter specialization of nonsymmetric Macdonald polynomials admits an explicit combinatorial formula in terms of quantum alcove paths, generalizing the formula of Lenart in the untwisted case. In particular, our formula yields a definition of quantum Bruhat graph for all affine root systems. For mixed type, the proof requires the Ram–Yip formula for the nonsymmetric Koornwinder polynomials. A quantum alcove path formula is also given at

Quiver Hall-Littlewood functions and Kostka-Shoji polynomials

t\rightarrow \infty

\epsilon=1

t→∞. As a consequence, we establish the positivity of the coefficients of nonsymmetric Macdonald polynomials under this limit, as conjectured by Cherednik and the first author. Finally, an explicit formula is given at