Matrix valued orthogonal polynomials for Gelfand pairs of rank one
| Autor: | M.L.A. van Pruijssen, Gert Heckman |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
multiplicity free branching
Rank (linear algebra) General Mathematics Geometry Universal enveloping algebra 01 natural sciences Combinatorics Matrix (mathematics) Lie algebra FOS: Mathematics 22E46 Representation Theory (math.RT) 0101 mathematics Mathematical Physics Mathematics 010102 general mathematics 33C47 Casimir element Differential operator Gelfand pair 010101 applied mathematics matrix valued orthogonal polynomials Spherical varieties of rank one Orthogonal polynomials ComputingMethodologies_DOCUMENTANDTEXTPROCESSING Mathematics - Representation Theory |
| Zdroj: | Tohoku Mathematical Journal, 68, 407-437 Tohoku Mathematical Journal, 68, 3, pp. 407-437 Tohoku Math. J. (2) 68, no. 3 (2016), 407-437 |
| ISSN: | 0040-8735 |
| DOI: | 10.2748/tmj/1474652266 |
| Popis: | In this paper we study matrix valued orthogonal polynomials of one variable associated with a compact connected Gelfand pair (G,K) of rank one, as a generalization of earlier work by Koornwinder and subsequently by Koelink, van Pruijssen and Roman for the pair (SU(2) x SU(2),SU(2)), and by Gr\"unbaum, Pacharoni and Tirao for the pair (SU(3),U(2)). Our method is based on representation theory using an explicit determination of the relevant branching rules. Our matrix valued orthogonal polynomials have the Sturm--Liouville property of being eigenfunctions of a second order matrix valued linear differential operator coming from the Casimir operator, and in fact are eigenfunctions of a commutative algebra of matrix valued linear differential operators coming from $U(g_c)^K$. Comment: 40 pages, 8 figures |
| Databáze: | OpenAIRE |
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