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Symmetry, Integrability and Geometry: Methods and Applications, 2009, Volume 5, 057, 18 pp.
DOI: https://doi.org/10.3842/SIGMA.2009.057 (Mi sigma403) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Dunkl Operators and Canonical Invariants of Reflection Groups

Arkady Berensteina, Yurii Burmanbc

a Department of Mathematics, University of Oregon, Eugene, OR 97403, USA
b Independent University of Moscow, 11 B. Vlassievsky per., 121002 Moscow, Russia
c Higher School of Economics, 20 Myasnitskaya Str., 101000 Moscow, Russia
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DOI: https://doi.org/10.3842/SIGMA.2009.057
Abstract: 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.
Keywords: Dunkl operators; reflection group.
Received: December 14, 2008; in final form May 21, 2009; Published online June 3, 2009
Bibliographic databases:
Document Type: Article
MSC: 20F55; 15A72
Language: English
Citation: Arkady Berenstein, Yurii Burman, “Dunkl Operators and Canonical Invariants of Reflection Groups”, SIGMA, 5 (2009), 057, 18 pp.
Citation in format AMSBIB
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