Submission: 2007, Jan 19
For a connected semisimple algebraic group $G$, we consider some special infinite series of tensor products of simple $G$-modules whose $G$-fixed point spaces are at most one-dimensional. We prove that their existence is closely related to the existence of open $G$-orbits in multiple flag varieties and address the problem of classifying such series.
2000 Mathematics Subject Classification: 20G05, 14L30
Keywords and Phrases: Semisimple group, tensor product of modules, orbit, weight, Weyl group
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