Geodesic
Commutative homogeneous spaces and co-isotropic symplectic actions
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 56 (2001) no. 1, pp. 1-60

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper is a survey of relationships among the following possible properties of a Riemannian homogeneous space $X=G/K$: Selberg's property of weak symmetry, commutativity of the algebra of $K$-invariant measures on $X$, commutativity of the algebra of $G$-invariant differential operators on $X$, commutativity of the Poisson algebra of $G$-invariant functions on the cotangent bundle of the space $X$, and (if $G$ is a reductive group) the property of the spectrum of the linear representation of the group $G$ on the algebra of polynomial functions on $X$ being multiplicity-free. Diverse results on structure and classification are presented, including the author's classification of irreducible Riemannian homogeneous spaces of Heisenberg type for which the Poisson algebra of invariant functions on the cotangent bundle is commutative. 
@article{RM_2001_56_1_a0,
     author = {\`E. B. Vinberg},
     title = {Commutative homogeneous spaces and co-isotropic symplectic actions},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {1--60},
     publisher = {mathdoc},
     volume = {56},
     number = {1},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RM_2001_56_1_a0/}
}
TY  - JOUR
AU  - È. B. Vinberg
TI  - Commutative homogeneous spaces and co-isotropic symplectic actions
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2001
SP  - 1
EP  - 60
VL  - 56
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/RM_2001_56_1_a0/
LA  - en
ID  - RM_2001_56_1_a0
ER  - 
%0 Journal Article
%A È. B. Vinberg
%T Commutative homogeneous spaces and co-isotropic symplectic actions
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2001
%P 1-60
%V 56
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/RM_2001_56_1_a0/
%G en
%F RM_2001_56_1_a0
È. B. Vinberg. Commutative homogeneous spaces and co-isotropic symplectic actions. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 56 (2001) no. 1, pp. 1-60. http://geodesic.mathdoc.fr/item/RM_2001_56_1_a0/