English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This note consists of two parts. The first part (\S 1 and \S 2) is a partialreview of the works by van Meer and Stokman (2010), van Meer (2011) and Stokman(2014) which established a bispectral analogue of the Cherednik correspondencebetween quantum affine Knizhnik-Zamolodchikov equations and the eigenvalueproblems of Macdonald type. In this review we focus on the rank one cases,i.e., on the reduced type $A_1$ and the non-reduced type $(C_1^\vee,C_1)$, towhich the associated Macdonald-Koornwinder polynomials are the Rogerspolynomials and the Askey-Wilson polynomials, respectively. We give detailedcomputations and formulas that may be difficult to find in the literature. Thesecond part (\S 3) is a complement of the first part, and is also acontinuation of our previous study (Y.-Y., 2022) on the parameterspecialization of Macdonald-Koornwinder polynomials, where we found four typesof specialization of the type $(C_1^\vee,C_1)$ parameters (which could becalled the Askey-Wilson parameters) to recover the type $A_1$. In this note, weshow that among the four specializations there is only one which is compatiblewith the bispectral correspondence discussed in the first part.

A review of rank one bispectral correspondence of quantum affine KZ equations and Macdonald-type eigenvalue problems