<i>c</i> -Functions and Koornwinder Polynomials

ABSTRACT This paper develops the theory of Macdonald–Koornwinder polynomials in parallel analogy with the work done by us in 2024 for the $GL_n$ case [c-functions and Macdonald polynomials, J. Algebra 655 (2024), 163–222]. In the context of the type $(C^\vee _n, C_n)$ 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.