Journal of Lie Theory

no. 2
Two Observations on Irreducible Representations of Groups
Journal of Lie Theory, Volume 12 (2002) no. 2, pp. 535-538
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).
DOI: 10.5802/jolt.280
Classification: 22E45
Keywords: Irreducible representations, orbits, algebraic groups, compact groups 
@article{JOLT_2002_12_2_a14,
     author = {J. Galindo and P. de la Harpe and T. Vust},
     title = {Two {Observations} on {Irreducible} {Representations} of {Groups}},
     journal = {Journal of Lie Theory},
     pages = {535--538},
     year = {2002},
     volume = {12},
     number = {2},
     doi = {10.5802/jolt.280},
     zbl = {0995.22002},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.280/}
}
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J. Galindo; P. de la Harpe; T. Vust. Two Observations on Irreducible Representations of Groups. Journal of Lie Theory, Volume 12 (2002) no. 2, pp. 535-538. doi: 10.5802/jolt.280

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