Dunkl Operators and Canonical Invariants of Reflection Groups

Details Dunkl Operators and Canonical Invariants of Reflection Groups Dunkl Operators and Canonical Invariants of Reflection Groups

2008-12-14

arxiv.org/abs/0812.2624v3

SIGMA 5 (2009), 057, 18 pages

Mathematics

Representation Theory

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

Scientific paper

10.3842/SIGMA.2009.057

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.

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