Hallnas-sigma12-049.pdf (690.61 kB)
Hermite and Laguerre symmetric functions associated with operators of Calogero-Moser-Sutherland type
journal contribution
posted on 2013-02-28, 15:18 authored by Patrick Desrosiers, Martin HallnasWe 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 socalled
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.
History
School
- Science
Department
- Mathematical Sciences
Citation
DESROSIERS, P. and HALLNÄS, M., 2012. Hermite and Laguerre symmetric functions associated with operators of Calogero-Moser-Sutherland type. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 8 (049), 51pp.Publisher
Institute of Mathematics of National Academy of Sciences of Ukraine © the authorsVersion
- VoR (Version of Record)
Publication date
2012Notes
This article was published in the journal, Symmetry, Integrability and Geometry : Methods and Applications (SIGMA) [© the authors] and is made available under published in SIGMA under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike Licence: http://creativecommons.org/licenses/by-nc-sa/3.0/ISSN
1815-0659eISSN
1815-0659Publisher version
Language
- en