Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Quantum Algebra

arXiv:math/0002090 (math)
[Submitted on 11 Feb 2000 (v1), last revised 18 Apr 2005 (this version, v2)]

Title:Koornwinder polynomials and affine Hecke algebras

Authors:J.V. Stokman
View PDF
Abstract: In this paper we derive the bi-orthogonality relations, diagonal term evaluations and evaluation formulas for the non-symmetric Koornwinder polynomials. For the derivation we use certain representations of the (double) affine Hecke algebra which were originally defined by Noumi and Sahi. The structure of the diagonal terms is clarified by expressing them as residues of the bi-orthogonality weight function. We furthermore give the explicit connection between the non-symmetric and the (anti-)symmetric theory.
Comments: 30 pages. Published version, with correction of a mistake in Theorem 3.4 (observed by Etingof, Gan and Oblomkov in math.QA/0504089)
Subjects: Quantum Algebra (math.QA); Representation Theory (math.RT)
MSC classes: 33D52; 33D80
Cite as: arXiv:math/0002090 [math.QA]
  (or arXiv:math/0002090v2 [math.QA] for this version)
  https://doi.org/10.48550/arXiv.math/0002090
Journal reference: Internat. Math. Res. Notices 2000, no. 19, 1006-1042

Submission history

From: Jasper V. Stokman [view email]
[v1] Fri, 11 Feb 2000 13:06:42 UTC (31 KB)
[v2] Mon, 18 Apr 2005 10:47:27 UTC (31 KB)
Full-text links:

Access Paper:

view license
Current browse context:
math.QA
< prev   |   next >
new | recent | 2000-02

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)