REVIEW 2 cited by
The Relationship between Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
read the original abstract
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.
Forward citations
Cited by 2 Pith papers
-
The dual pair $\big(U_q(\mathfrak{su}(1,1)),\mathfrak{o}_{q^{1/2}}(2n)\big)$, $q$-oscillators and Askey-Wilson algebras
The Askey-Wilson algebra AW(n) arises not only from tensor products of U_q(su(1,1)), but also as the commutant of n commuting rotations in q-oscillator representations of o_{q^{1/2}}(2n), and the two descriptions are ...
-
Automorphisms of the DAHA of type $\check{C_1}C_1$ and non-symmetric Askey-Wilson functions
Automorphisms of DAHA type check C1 C1 map Askey-Wilson polynomials to functions and produce a symmetric plus anti-symmetric expression for the non-symmetric Askey-Wilson function.
Discussion (0). Continue with ORCID to comment.