This paper derives c-function formulas and examines Koornwinder polynomials in relation to other root systems, suggesting new insights into classical polynomial theory.
This paper develops the theory of Macdonald–Koornwinder polynomials in parallel analogy with the work done by us in 2024 for the GLₙ case [c-functions and Macdonald polynomials, J. Algebra 655 (2024), 163–222]. In the context of the type (C^ ₙ, Cₙ) 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.
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Colmenarejo et al. (2025) studied this question.
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