Journal of Lie Theory, Vol. 11, No. 2, pp. 441-458 (2001)

Invariant Theory for the Orthogonal Group via Star Products

Didier Arnal, Oumarou Boukary Baoua, Chal Benson, and Gail Ratcliff

Département de Mathématiques
Université de Metz
Ile du Saulcy 57045
Metz cedex 01
France
arnal@poncelet.univ-metz.fr
boukary@poncelet.univ-metz.fr
and
Dept. of Math. and Comp. Science
Univ. of Missouri-St. Louis
St. Louis, MO 63121
U.S.A.
benson@arch.umsl.edu
ratcliff@arch.umsl.edu

Abstract: In this paper we apply star products to the invariant theory for multiplicity free actions. The space of invariants for a compact linear multiplicity free action has two canonical bases which are orthogonal with respect to two different inner products. One of these arises in connection with the star product. We use this fact to determine the elements in the canonical bases for the invariants under the action of $SO(n, R)\times T$ on $ C^n$. The formulae obtained improve prior results due to the last two authors and Jenkins.

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