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Vector-Valued Jack Polynomials from Scratch
Репозиторій DSpace/Manakin
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- Фізико-технічні та математичні науки
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- Відділення математики
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7
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- Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7, випуск за цей рік
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Vector-Valued Jack Polynomials from Scratch
Посилання:
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.
Підтримка:
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.
Дата:
2011
Переглядів:
697
Завантажень:
262
Анотація:
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.
