Symmetry, Integrability and Geometry: Methods and Applications (Jun 2009)
Dunkl Operators and Canonical Invariants of Reflection Groups
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.