Orthogonal polynomials associated with root systems
| dc.creator | Macdonald, Ian G. | |
| dc.date | 2000-11-08 | |
| dc.date.accessioned | 2026-07-07T04:38:29Z | |
| dc.date.available | 2026-07-07T04:38:29Z | |
| dc.description | Let R and S be two irreducible root systems spanning the same vector space and having the same Weyl group W, such that S (but not necessarily R) is reduced. For each such pair (R,S) we construct a family of W-invariant orthogonal polynomials in several variables, whose coefficients are rational functions of parameters $q,t_1,t_2,...,t_r$, where r (=1,2 or 3) is the number of W-orbits in R. For particular values of these parameters, these polynomials give the values of zonal spherical functions on real and p-adic symmetric spaces. Also when R=S is of type $A_n$, they conincide with the symmetric polynomials described in I. G. Macdonald, Symmetric Functions and Hall Polynomials, 2nd edition, Oxford University Press (1995), Chapter VI. | |
| dc.description | 40 pages, AmS-TeX. This is the 1987 preprint of the same title that has been circulated privately only as a handwritten manuscript. It has now been typed and published in the Séminaire Lotharingien de Combinatoire | |
| dc.identifier | https://arxiv.org/abs/math/0011046 | |
| dc.identifier | http://arxiv.org/abs/math/0011046 | |
| dc.identifier | Séminaire Lotharingien Combin. 45 (2000), Article B45a, 40 pp | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60298 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Combinatorics | |
| dc.title | Orthogonal polynomials associated with root systems | |
| dc.type | text |