Macdonald Polynomials of Type Cₙ with One-Column Diagrams and Deformed Catalan Numbers

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2018
• Main Authors: Hoshino, A., Shiraishi, J.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2018
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/209856
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Macdonald Polynomials of Type Cₙ with One-Column Diagrams and Deformed Catalan Numbers / A. Hoshino, J. Shiraishi // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 22 назв. — англ.

We present an explicit formula for the transition matrix C from the type Cₙ degeneration of the Koornwinder polynomials P₍₁ᵣ₎(x|a,−a,c,−c|q,t) with one column diagrams, to the type Cₙ monomial symmetric polynomials m₍₁ᵣ₎(x). The entries of the matrix C enjoy a set of three-term recursion relations,...