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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| Дата: | 2012 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2012
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148381 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
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irk-123456789-1483812019-02-19T01:24:58Z Hermite and Laguerre Symmetric Functions Associated with Operators of Calogero-Moser-Sutherland Type Desrosiers, P. Hallnäs, M. 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. 2012 Article 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 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Desrosiers, P. Hallnäs, M. |
| spellingShingle |
Desrosiers, P. Hallnäs, M. Hermite and Laguerre Symmetric Functions Associated with Operators of Calogero-Moser-Sutherland Type Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Desrosiers, P. Hallnäs, M. |
| author_sort |
Desrosiers, P. |
| title |
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_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_sort |
hermite and laguerre symmetric functions associated with operators of calogero-moser-sutherland type |
| publisher |
Інститут математики НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148381 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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