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dc.contributor.author
N. Aldenhoven
dc.contributor.author
Koelink, Hendrik Tjerk
dc.contributor.author
Román, Pablo Manuel
dc.date.available
2018-10-16T20:36:29Z
dc.date.issued
2017-06
dc.identifier.citation
N. Aldenhoven; Koelink, Hendrik Tjerk; Román, Pablo Manuel; Matrix-valued orthogonal polynomials related to the quantum analogue of (SU (2) × SU (2) , diag); Springer; Ramanujan Journal; 43; 2; 6-2017; 243-311
dc.identifier.issn
1382-4090
dc.identifier.uri
http://hdl.handle.net/11336/62509
dc.description.abstract
Matrix-valued spherical functions related to the quantum symmetric pair for the quantum analogue of (SU (2) × SU (2) , diag) are introduced and studied in detail. The quantum symmetric pair is given in terms of a quantised universal enveloping algebra with a coideal subalgebra. The matrix-valued spherical functions give rise to matrix-valued orthogonal polynomials, which are matrix-valued analogues of a subfamily of Askey–Wilson polynomials. For these matrix-valued orthogonal polynomials, a number of properties are derived using this quantum group interpretation: the orthogonality relations from the Schur orthogonality relations, the three-term recurrence relation and the structure of the weight matrix in terms of Chebyshev polynomials from tensor product decompositions, and the matrix-valued Askey–Wilson type q-difference operators from the action of the Casimir elements. A more analytic study of the weight gives an explicit LDU-decomposition in terms of continuous q-ultraspherical polynomials. The LDU-decomposition gives the possibility to find explicit expressions of the matrix entries of the matrix-valued orthogonal polynomials in terms of continuous q-ultraspherical polynomials and q-Racah polynomials.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Springer
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Continuous Q-Ultraspherical Polynomials
dc.subject
Matrix-Valued Orthogonal Polynomials
dc.subject
Q-Racah Polynomials
dc.subject
Quantum Groups
dc.subject
Quantum Symmetric Pairs
dc.subject
Spherical Functions
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
Matrix-valued orthogonal polynomials related to the quantum analogue of (SU (2) × SU (2) , diag)
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2018-10-12T18:38:30Z
dc.journal.volume
43
dc.journal.number
2
dc.journal.pagination
243-311
dc.journal.pais
Alemania
dc.journal.ciudad
Berlin
dc.description.fil
Fil: N. Aldenhoven. Radboud Universiteit Nijmegen; Países Bajos
dc.description.fil
Fil: Koelink, Hendrik Tjerk. Radboud Universiteit Nijmegen; Países Bajos
dc.description.fil
Fil: Román, Pablo Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
dc.journal.title
Ramanujan Journal
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/https://dx.doi.org/10.1007/s11139-016-9788-y
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s11139-016-9788-y
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