Journal of Lie Theory

no. 2
Multiplicity Free Spaces with a One-Dimensional Quotient
Journal of Lie Theory, Volume 23 (2013) no. 2, pp. 433-458
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.
DOI: 10.5802/jolt.732
Classification: 14L30, 11S90, 22E46
Keywords: Multiplicity free spaces, one dimensional quotient, prehomogeneous vector spaces 
@article{JOLT_2013_23_2_a4,
     author = {H. Rubenthaler},
     title = {Multiplicity {Free} {Spaces} with a {One-Dimensional} {Quotient}},
     journal = {Journal of Lie Theory},
     pages = {433--458},
     year = {2013},
     volume = {23},
     number = {2},
     doi = {10.5802/jolt.732},
     zbl = {1273.14095},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.732/}
}
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H. Rubenthaler. Multiplicity Free Spaces with a One-Dimensional Quotient. Journal of Lie Theory, Volume 23 (2013) no. 2, pp. 433-458. doi: 10.5802/jolt.732

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