Mathematics – Quantum Algebra
Scientific paper
2006-12-22
SIGMA 3 (2007), 063, 15 pages
Mathematics
Quantum Algebra
This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Sym
Scientific paper
10.3842/SIGMA.2007.063
Zhedanov's algebra AW(3) is considered with explicit structure constants such that, in the basic representation, the first generator becomes the second order q-difference operator for the Askey-Wilson polynomials. It is proved that this representation is faithful for a certain quotient of AW(3) such that the Casimir operator is equal to a special constant. Some explicit aspects of the double affine Hecke algebra (DAHA) related to symmetric and non-symmetric Askey-Wilson polynomials are presented and proved without requiring knowledge of general DAHA theory. Finally a central extension of this quotient of AW(3) is introduced which can be embedded in the DAHA by means of the faithful basic representations of both algebras.
No associations
LandOfFree
The Relationship between Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Relationship between Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Relationship between Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-380028