Journal of Lie Theory 11 (2001), No. 2, 441--458
Copyright Heldermann Verlag 2001
Invariant Theory for the Orthogonal Group via Star Products
Didier Arnal
Dép. de Mathématiques, Université de Metz, Ile du Saulcy, 57045 Metz 01, France
Oumarou Boukary Baoua
Dép. de Mathématiques, Université de Metz, Ile du Saulcy, 57045 Metz 01, France
Chal Benson
Dept. of Mathematics and Computer Science, University of Missouri, St. Louis, MO 63121, U.S.A.
Gail Ratcliff
Dept. of Mathematics and Computer Science, University of Missouri, St. Louis, MO 63121, U.S.A.
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) ´T on Cn. The formulae obtained improve prior results due to the last two authors and Jenkins.
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