Journal of Lie Theory

no. 2
Invariant Theory for the Orthogonal Group via Star Products
Journal of Lie Theory, Volume 11 (2001) no. 2, pp. 441-458
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.
DOI: 10.5802/jolt.241
Classification: 22E46, 22E30, 43A80
Keywords: Lie group action, Fock inner product, star inner product, star products, invariant theory, Heisenberg group, Gelfand pair 
@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},
     doi = {10.5802/jolt.241},
     zbl = {0977.22007},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.241/}
}
TY  - JOUR
AU  - D. Arnal
AU  - O. B. Baoua
AU  - C. Benson
AU  - G. Ratcliff
TI  - Invariant Theory for the Orthogonal Group via Star Products
JO  - Journal of Lie Theory
PY  - 2001
SP  - 441
EP  - 458
VL  - 11
IS  - 2
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.241/
DO  - 10.5802/jolt.241
ID  - JOLT_2001_11_2_a8
ER  - 
%0 Journal Article
%A D. Arnal
%A O. B. Baoua
%A C. Benson
%A G. Ratcliff
%T Invariant Theory for the Orthogonal Group via Star Products
%J Journal of Lie Theory
%D 2001
%P 441-458
%V 11
%N 2
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.241/
%R 10.5802/jolt.241
%F JOLT_2001_11_2_a8
D. Arnal; O. B. Baoua; C. Benson; G. Ratcliff. Invariant Theory for the Orthogonal Group via Star Products. Journal of Lie Theory, Volume 11 (2001) no. 2, pp. 441-458. doi: 10.5802/jolt.241

Cited by Sources: