Koornwinder polynomials and affine Hecke algebras
By Jasper V. Stokman. 2000
52 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/5c59a1887c943a6b89466365b3270ddcd5432420
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In Applied Mathematics
- Pavel Etingof
- Eric M. Rains
- Tom H. Koornwinder
- Alexei Oblomkov
- V. Spiridonov
- G. Vartanov
- Luís Daniel Abreu
- Thomas Ernst
In Mathematical Physics
- Tom H. Koornwinder
- Alexei Oblomkov
- Pavel Etingof
- Eric M. Rains
- I. Gordon
- Alexei Borodin
- I. Losev
- V. Ginzburg
In Statistical and Nonlinear Physics
- Alexei Oblomkov
- Pavel Etingof
- Eric M. Rains
- Tom H. Koornwinder
- V. Spiridonov
- I. Gordon
- V. Ginzburg
- D. Nikshych
Citations in the corpus
- BCn-symmetric polynomials (2001, unknown): “We could of course simply refer to the proofs in the literature [27, 22, 23] that the usual Koornwinder polynomials satisfy evaluation symmetry; instead, we will give a direct proof (in particular, avoiding any use of double affine Hecke algebra machinery).”
- Generalized double affine Hecke algebras of rank 1 and quantized del Pezzo surfaces (2004, methodology): “In the D4 case, it is the double affine Hecke algebra of type C∨C1 of Sahi, Noumi and Stokman [Sa, St, NoSt].”
- Cherednik and Hecke algebras of varieties with a finite group action (2004, methodology): “The fact that this algebra is flat was proved by Cherednik, Sahi, Noumi, Stokman (see [Ch],[Sa],[NoSt],[ St ]) using a different approach (q-deformed Dunkl operators).”
- The Relationship between Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case (2006, background): “I also thank Jasper Stokman for helpful comments.”