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Please use this identifier to cite or link to this item: http://dspace.utalca.cl/handle/1950/8987

Title: Hermite and Laguerre Symmetric Functions Associated with Operators of Calogero-Moser-Sutherland Type
Authors: Desrosiers, P.
Hallnas, M.
Keywords: symmetric functions
super-symmetric polynomials
(deformed) Calogero-Moser-Sutherland models
Issue Date: 2012
Publisher: NATL ACAD SCI UKRAINE, INST MAT
Citation: SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS Volume: 8 Article Number: 049 DOI: 10.3842/SIGMA.2012.049
Abstract: We introduce and study natural generalisations of the Hermite and Laguerre polynomials in the ring of symmetric functions as eigenfunctions of infinite-dimensional analogues of partial differential operators of Calogero-Moser-Sutherland (CMS) type. In particular, we obtain generating functions, duality relations, limit transitions from Jacobi symmetric functions, and Pieri formulae, as well as the integrability of the corresponding operators. We also determine all ideals in the ring of symmetric functions that are spanned by either Hermite or Laguerre symmetric functions, and by restriction of the corresponding infinite-dimensional CMS operators onto quotient rings given by such ideals we obtain so-called deformed CMS operators. As a consequence of this restriction procedure, we deduce, in particular, infinite sets of polynomial eigenfunctions, which we shall refer to as super Hermite and super Laguerre polynomials, as well as the integrability, of these deformed CMS operators. We also introduce and study series of a generalised hypergeometric type, in the context of both symmetric functions and 'super' polynomials.
Description: Desrosiers, P (reprint author), Univ Talca, Inst Matemat & Fis, 2 Norte 685, Talca, Chile.
URI: http://dspace.utalca.cl/handle/1950/8987
ISSN: 1815-0659
Appears in Collections:Artículos en publicaciones ISI - Universidad de Talca

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