Journal of Lie Theory 12 (2002), No. 2, 535--538
Copyright Heldermann Verlag 2002
Two Observations on Irreducible Representations of Groups
Jorge Galindo
Dep. de Matemáticas, Universidad Jaume I, 8029-AP Castellón, Spain
Pierre de la Harpe
Section de Mathématiques, Université de Genève, 1211 Genève 24, Switzerland
Thierry Vust
Section de Mathématiques, Université de Genève, 1211 Genève 24, Switzerland
For an irreducible representation of a connected affine algebraic group G in a vector space V of dimension at least 2, it is shown that the intersection of any orbit π(G)x (with x in V) and any hyperplane of V is non-empty. The question is raised to decide whether an analogous fact holds for irreducible continuous representations of connected compact groups, for example of SU(2).
Keywords: Irreducible representations, orbits, algebraic groups, compact groups.
MSC: 22E45
[ Fulltext-pdf (143 KB)]