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Matrix-valued orthogonal polynomials rel...
Aldenhoven, Noud...

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Matrix-valued orthogonal polynomials related to the quantum analogue of (SU(2)×SU(2),diag) by Aldenhoven, Noud ( Author )
Lemonjar Open Access
N.A
13-07-2015
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, 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.
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English
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MYR 0.00
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https://arxiv.org/abs/1507.03426
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