Dunkl Operators and Canonical Invariants of Reflection Groups

Dunkl Operators and Canonical Invariants of Reflection Groups

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 g...

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Bibliographic Details
Main Authors: Arkady Berenstein, Yurii Burman
Format: Article
Language:English
Published: National Academy of Science of Ukraine 2009-06-01
Series:Symmetry, Integrability and Geometry: Methods and Applications
Subjects:
Dunkl operators
reflection group
Online Access:http://dx.doi.org/10.3842/SIGMA.2009.057
Description
Summary: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.
ISSN:1815-0659

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