Hermite and Laguerre Symmetric Functions Associated with Operators of Calogero-Moser-Sutherland Type
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Hermite and Laguerre Symmetric Functions Associated with Operators of Calogero-Moser-Sutherland Type
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| Creator |
Desrosiers, P.
Hallnäs, M. |
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| Description |
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.
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| Date |
2019-02-18T11:12:08Z
2019-02-18T11:12:08Z 2012 |
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| Type |
Article
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| Identifier |
Hermite and Laguerre Symmetric Functions Associated with Operators of Calogero-Moser-Sutherland Type / P. Desrosiers, M. Hallnäs // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 48 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 05E05; 13J05; 81R12 DOI: http://dx.doi.org/10.3842/SIGMA.2012.049 http://dspace.nbuv.gov.ua/handle/123456789/148381 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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