c-functions and Koornwinder polynomials

2024/10/25 by Colmenarejo, Laura, Ram, Arun
#05E05 (Primary) #33D52 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2410.19957

Abstract

This paper develops the theory of Macdonald-Koornwinder polynomials in parallel analogy with the work done for the GL_n case in [CR22]. In the context of the type CC_n affine root system the Macdonald polynomials of other root systems of classical type are specializations of the Koornwinder polynomials. We derive c-function formulas for symmetrizers and use them to give E-expansions, principal specializations and norm formulas for bosonic, mesonic and fermionic Koornwinder polynomials. Finally, we explain the proof of the norm conjectures and constant term conjectures for the Koornwinder case.

Related

• Specializing Koornwinder polynomials to Macdonald polynomials of type B,C,D and B C
• Macdonald-Koornwinder polynomials
• c-functions and Macdonald polynomials
• A Littlewood-Richardson rule for Koornwinder polynomials
• A difference-integral representation of Koornwinder polynomials