Séminaire Lotharingien de Combinatoire, B50j (2005), 47 pp.
Adriano Garsia and Nolan Wallach
Some New Applications of Orbit Hamonics
We prove a new result in the Theory of Orbit Harmonics and
derive from it a new proof of the Cohen-Macauliness of the ring
QIm(G) of m-Quasi-Invariants
of a Coxeter Group G.
Using the non-degeneracy of the fundamental bilinear form on
this approach yields also a direct and simple proof that the
quotient of QIm(G) by the ideal generated by
the homogeneous G-invariants affords a graded version of the
left regular representation of G.
Originally all of these results were obtained as
a combination of some deep work of Etingof-Ginzburg ,
Feigin-Veselov  and Felder-Veselov .
The arguments here are quite elementary and self contained, except
those using the non-degeneracy of the fundamental bilinear
Received: November 20, 2004.
Accepted: January 14, 2005.
Final Version: January 29, 2005.
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