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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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