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Dunkl Operators and Canonical Invariants of Reflection Groups
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2009, том 5
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Dunkl Operators and Canonical Invariants of Reflection Groups
Інший ID:
2000 Mathematics Subject Classification: 20F55; 15A72
Посилання:
Dunkl Operators and Canonical Invariants of Reflection Groups / A. Berenstein, Y. Burman // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 20 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue on Dunkl Operators and Related Topics. The work was partially supported by the CRDF grant RUM1-2895-MO-07. The second author was also supported by the INTAS grant 05-7805, RFBR grants 08-01-00110-a and NSh709.2008.1, and the HSE Scientific Foundation grant 08-01-0019. The authors are grateful to P. Etingof, M. Feigin, A. Samokhin, and Y. Xu for valuable discussions. The second author wishes to thank the University of Oregon, where most of this work was carried out, for its warm hospitality.
Дата:
2009
Переглядів:
356
Завантажень:
210
Анотація:
Using Dunkl operators, we introduce a continuous family of canonical invariants of finite reflection groups. We verify that the elementary canonical invariants of the symmetric group are deformations of the elementary symmetric polynomials. We also compute the canonical invariants for all dihedral groups as certain hypergeometric functions.
