Multiplicity free spaces with a one dimensional quotient

Hubert Rubenthaler (1)

1 IRMA - Institut de Recherche Mathématique Avancée

The multiplicity free spaces with a one dimensional quotient were introduced by Thierry Levasseur in [11]. 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 ([17]). 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.

Mots clés: multiplicity free spaces; prehomogeneous vector spaces

Domaines: Théorie des représentations [math.RT]

Hubert Rubenthaler. Multiplicity free spaces with a one dimensional quotient. Journal of Lie Theory, 2013, 23 (2), pp.433-458. ⟨hal-00693353⟩