Hermite and Laguerre Symmetric Functions Associated with Operators of Calogero-Moser-Sutherland Type
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, dual...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2012 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2012
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/148381 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862642790960201728 |
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| author | Desrosiers, P. Hallnäs, M. |
| author_facet | Desrosiers, P. Hallnäs, M. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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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| first_indexed | 2025-12-01T07:30:15Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148381 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-01T07:30:15Z |
| publishDate | 2012 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Desrosiers, P. Hallnäs, M. 2019-02-18T11:12:08Z 2019-02-18T11:12:08Z 2012 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 https://nasplib.isofts.kiev.ua/handle/123456789/148381 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. The work of P.D. was supported by FONDECYT grant #1090034 and by CONICYT through
 the Anillos de Investigaci´on RED4 y ACT56. M.H. would like to thank O. Chalykh, S.N.M. Ruijsenaars and A.P. Veselov for helpful discussions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Hermite and Laguerre Symmetric Functions Associated with Operators of Calogero-Moser-Sutherland Type Article published earlier |
| spellingShingle | Hermite and Laguerre Symmetric Functions Associated with Operators of Calogero-Moser-Sutherland Type Desrosiers, P. Hallnäs, M. |
| title | Hermite and Laguerre Symmetric Functions Associated with Operators of Calogero-Moser-Sutherland Type |
| title_full | Hermite and Laguerre Symmetric Functions Associated with Operators of Calogero-Moser-Sutherland Type |
| title_fullStr | Hermite and Laguerre Symmetric Functions Associated with Operators of Calogero-Moser-Sutherland Type |
| title_full_unstemmed | Hermite and Laguerre Symmetric Functions Associated with Operators of Calogero-Moser-Sutherland Type |
| title_short | Hermite and Laguerre Symmetric Functions Associated with Operators of Calogero-Moser-Sutherland Type |
| title_sort | hermite and laguerre symmetric functions associated with operators of calogero-moser-sutherland type |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148381 |
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