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.

v2: few corrections, some proofs and references added; v3: published version