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/

Zendy Plus

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

Zendy Tools

Zendy Open

Koornwinder polynomials are a 6-parameter BC_n-symmetric family of Laurentpolynomials indexed by partitions, from which Macdonald polynomials can berecovered in suitable limits of the parameters. As in the Macdonald polynomialcase, standard constructions via difference operators do not allow one todirectly control these polynomials at q=0. In the first part of this paper, weprovide an explicit construction for these polynomials in this limit, using thedefining properties of Koornwinder polynomials. Our formula is a first step indeveloping the analogy between Hall-Littlewood polynomials and Koornwinderpolynomials at q=0. Next, we provide an analogous construction for thenonsymmetric Koornwinder polynomials in the same limiting case. The methodemployed in this paper is a BC-type adaptation of techniques used in an earlierwork of the author, which gave a combinatorial method for proving vanishingresults of Rains and Vazirani at the Hall-Littlewood level. As a consequence ofthis work, we obtain direct arguments for the constant term evaluations andnorms in both the symmetric and nonsymmetric cases.

Symmetric and nonsymmetric Hall-Littlewood polynomials of type BC