Vector-Valued Jack Polynomials from Scratch
Vector-valued Jack polynomials associated to the symmetric group SN are polynomials with multiplicities in an irreducible module of SN and which are simultaneous eigenfunctions of the Cherednik-Dunkl operators with some additional properties concerning the leading monomial. These polynomials were in...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2011 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2011
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/146782 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Vector-Valued Jack Polynomials from Scratch / C.F. Dunkl, J. Luque // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 18 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862735287085432832 |
|---|---|
| author | Dunkl, C.F. Luque, J. |
| author_facet | Dunkl, C.F. Luque, J. |
| citation_txt | Vector-Valued Jack Polynomials from Scratch / C.F. Dunkl, J. Luque // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 18 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Vector-valued Jack polynomials associated to the symmetric group SN are polynomials with multiplicities in an irreducible module of SN and which are simultaneous eigenfunctions of the Cherednik-Dunkl operators with some additional properties concerning the leading monomial. These polynomials were introduced by Griffeth in the general setting of the complex reflections groups G(r,p,N) and studied by one of the authors (C. Dunkl) in the specialization r=p=1 (i.e. for the symmetric group). By adapting a construction due to Lascoux, we describe an algorithm allowing us to compute explicitly the Jack polynomials following a Yang-Baxter graph. We recover some properties already studied by C. Dunkl and restate them in terms of graphs together with additional new results. In particular, we investigate normalization, symmetrization and antisymmetrization, polynomials with minimal degree, restriction etc. We give also a shifted version of the construction and we discuss vanishing properties of the associated polynomials.
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| first_indexed | 2025-12-07T19:48:03Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146782 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:48:03Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Dunkl, C.F. Luque, J. 2019-02-11T15:05:28Z 2019-02-11T15:05:28Z 2011 Vector-Valued Jack Polynomials from Scratch / C.F. Dunkl, J. Luque // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 18 назв. — англ. 1815-0659 https://nasplib.isofts.kiev.ua/handle/123456789/146782 Vector-valued Jack polynomials associated to the symmetric group SN are polynomials with multiplicities in an irreducible module of SN and which are simultaneous eigenfunctions of the Cherednik-Dunkl operators with some additional properties concerning the leading monomial. These polynomials were introduced by Griffeth in the general setting of the complex reflections groups G(r,p,N) and studied by one of the authors (C. Dunkl) in the specialization r=p=1 (i.e. for the symmetric group). By adapting a construction due to Lascoux, we describe an algorithm allowing us to compute explicitly the Jack polynomials following a Yang-Baxter graph. We recover some properties already studied by C. Dunkl and restate them in terms of graphs together with additional new results. In particular, we investigate normalization, symmetrization and antisymmetrization, polynomials with minimal degree, restriction etc. We give also a shifted version of the construction and we discuss vanishing properties of the associated polynomials. The authors are grateful to A. Lascoux for fruitful discussions about the Yang–Baxter Graphs.
 The authors acknowledge the referees for their meticulous reading and valuable comments. This paper is partially supported by the ANR project PhysComb, ANR-08-BLAN-0243-04. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Vector-Valued Jack Polynomials from Scratch Article published earlier |
| spellingShingle | Vector-Valued Jack Polynomials from Scratch Dunkl, C.F. Luque, J. |
| title | Vector-Valued Jack Polynomials from Scratch |
| title_full | Vector-Valued Jack Polynomials from Scratch |
| title_fullStr | Vector-Valued Jack Polynomials from Scratch |
| title_full_unstemmed | Vector-Valued Jack Polynomials from Scratch |
| title_short | Vector-Valued Jack Polynomials from Scratch |
| title_sort | vector-valued jack polynomials from scratch |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146782 |
| work_keys_str_mv | AT dunklcf vectorvaluedjackpolynomialsfromscratch AT luquej vectorvaluedjackpolynomialsfromscratch |