Geodesic
Multiplicity Free Spaces with a One-Dimensional Quotient
Journal of Lie theory, Tome 23 (2013) no. 2, pp. 433-458

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The multiplicity free spaces with a one dimensional quotient were introduced by Thierry Levasseur ["Radial components, prehomogeneous vector spaces, and rational Cherednik algebras", Int. Math. Res. Not. IMRN 2009, no 3, 462--511]. Recently, the author has shown that the algebra of differential operators on such spaces which are invariant under the semi-simple part of the group is a Smith algebra ["Invariant differential operators on a class of multiplicity free spaces", arXiv:1103.1721v1 (math.RT)]. We give here the classification of these spaces which are indecomposable, up to geometric equivalence. We also investigate whether or not these spaces are regular or of parabolic type as a prehomogeneous vector space.
Classification : 14L30, 11S90, 22E46
Mots-clés : Multiplicity free spaces, one dimensional quotient, prehomogeneous vector spaces 
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     author = {H. Rubenthaler },
     title = {Multiplicity {Free} {Spaces} with a {One-Dimensional} {Quotient}},
     journal = {Journal of Lie theory},
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     number = {2},
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H. Rubenthaler . Multiplicity Free Spaces with a One-Dimensional Quotient. Journal of Lie theory, Tome 23 (2013) no. 2, pp. 433-458. http://geodesic.mathdoc.fr/item/JLT_2013_23_2_JLT_2013_23_2_a4/