Askey–Wilson algebra
E653520
The Askey–Wilson algebra is a quadratic algebra arising in the theory of orthogonal polynomials and quantum groups, closely linked to the Askey–Wilson polynomials and related integrable models.
Statements (45)
| Predicate | Object |
|---|---|
| instanceOf |
associative algebra
ⓘ
quadratic algebra ⓘ |
| appearsIn |
algebraic combinatorics
ⓘ
theory of bispectral problems ⓘ |
| arisesIn |
exactly solvable models
ⓘ
integrable lattice models ⓘ representation theory of quantum groups ⓘ theory of orthogonal polynomials ⓘ |
| definingRelations | quadratic relations among generators A, B, C ⓘ |
| field | mathematics ⓘ |
| generalizes | algebras associated with classical orthogonal polynomials ⓘ |
| hasCenter | central elements depending on parameters ⓘ |
| hasGenerator |
A
ⓘ
B ⓘ C ⓘ |
| hasRealization |
operators acting on polynomial spaces
ⓘ
q-difference operators ⓘ |
| hasRepresentation |
finite-dimensional modules
ⓘ
infinite-dimensional modules ⓘ |
| namedAfter |
James A. Wilson
NERFINISHED
ⓘ
Richard Askey NERFINISHED ⓘ |
| parameterDependsOn |
q
ⓘ
structure constants ⓘ |
| relatedConcept |
Askey scheme
NERFINISHED
ⓘ
q-Askey scheme NERFINISHED ⓘ |
| relatedTo |
Askey–Wilson polynomials
NERFINISHED
ⓘ
Leonard pairs NERFINISHED ⓘ U_q(sl_2) NERFINISHED ⓘ double affine Hecke algebras NERFINISHED ⓘ q-Racah polynomials NERFINISHED ⓘ q-orthogonal polynomials ⓘ quantum groups ⓘ quantum integrable models ⓘ tridiagonal pairs ⓘ |
| structure | defined by quadratic commutation relations ⓘ |
| subfield |
algebra
ⓘ
integrable systems ⓘ orthogonal polynomials ⓘ quantum groups ⓘ |
| symmetryAlgebraOf |
Askey–Wilson polynomials
NERFINISHED
ⓘ
certain q-hypergeometric operators ⓘ |
| usedFor |
algebraic description of Askey–Wilson polynomials
ⓘ
classification of tridiagonal pairs ⓘ construction of Leonard pairs ⓘ spectral analysis of q-difference operators ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.