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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.doi:10.3842/sigma.2009.057 fatcat:xlfatwrqrrd4xicxow52rmvcie