Geodesic
Invariant Theory for the Orthogonal Group via Star Products
Journal of Lie Theory, Tome 11 (2001) no. 2, pp. 441-458

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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.
Classification : 22E46, 22E30, 43A80
Mots-clés : Lie group action, Fock inner product, star inner product, star products, invariant theory, Heisenberg group, Gelfand pair 
D. Arnal; O. B. Baoua; C. Benson; G. Ratcliff. Invariant Theory for the Orthogonal Group via Star Products. Journal of Lie Theory, Tome 11 (2001) no. 2, pp. 441-458. http://geodesic.mathdoc.fr/item/JOLT_2001_11_2_a8/
@article{JOLT_2001_11_2_a8,
     author = {D. Arnal and O. B. Baoua and C. Benson and G. Ratcliff},
     title = {Invariant {Theory} for the {Orthogonal} {Group} via {Star} {Products}},
     journal = {Journal of Lie Theory},
     pages = {441--458},
     year = {2001},
     volume = {11},
     number = {2},
     zbl = {0977.22007},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2001_11_2_a8/}
}
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