Orthogonal polynomials associated with root systems

dc.creatorMacdonald, Ian G.
dc.date2000-11-08
dc.date.accessioned2026-07-07T04:38:29Z
dc.date.available2026-07-07T04:38:29Z
dc.descriptionLet 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.description40 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.identifierhttps://arxiv.org/abs/math/0011046
dc.identifierhttp://arxiv.org/abs/math/0011046
dc.identifierSéminaire Lotharingien Combin. 45 (2000), Article B45a, 40 pp
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60298
dc.subjectQuantum Algebra
dc.subjectClassical Analysis and ODEs
dc.subjectCombinatorics
dc.titleOrthogonal polynomials associated with root systems
dc.typetext

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