Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 5 (2009), 057, 18 pages      arXiv:0812.2624      https://doi.org/10.3842/SIGMA.2009.057
Contribution to the Special Issue on Dunkl Operators and Related Topics

Dunkl Operators and Canonical Invariants of Reflection Groups

Arkady Berenstein a and Yurii Burman b, c
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

Received December 14, 2008, in final form May 21, 2009; Published online June 03, 2009

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.

Key words: Dunkl operators; reflection group.

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