Laguerre functions and representations of su(1,1)
| dc.creator | Groenevelt, Wolter | |
| dc.date | 2003-02-27 | |
| dc.date.accessioned | 2026-07-07T07:36:34Z | |
| dc.date.available | 2026-07-07T07:36:34Z | |
| dc.description | Spectral analysis of a certain doubly infinite Jacobi operator leads to orthogonality relations for confluent hypergeometric functions, which are called Laguerre functions. This doubly infinite Jacobi operator corresponds to the action of a parabolic element of the Lie algebra $\mathfrak{su}(1,1)$. The Clebsch-Gordan coefficients for the tensor product representation of a positive and a negative discrete series representation of $\mathfrak{su}(1,1)$ are determined for the parabolic bases. They turn out to be multiples of Jacobi functions. From the interpretation of Laguerre polynomials and functions as overlap coefficients, we obtain a product formula for the Laguerre polynomials, given by a discontinuous integral over Laguerre functions, Jacobi functions and continuous dual Hahn polynomials. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/math/0302342 | |
| dc.identifier | http://arxiv.org/abs/math/0302342 | |
| dc.identifier | Indag. Math. (N.S.) 14 (2003), no. 3-4, 329-352 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120474 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Representation Theory | |
| dc.title | Laguerre functions and representations of su(1,1) | |
| dc.type | text |