Tensor product decompositions and open orbits in multiple flag varieties

Details Tensor product decompositions and open orbits in multiple flag varieties Tensor product decompositions and open orbits in multiple flag varieties

2006-08-31

arxiv.org/abs/math/0609003v5

J. Algebra, Vol. 313 (2007), 392-416

Mathematics

Representation Theory

23 pages. Footnote on upper bounds of separation indices of root systems is added (p. 15). In Example 11 some recent results a

Scientific paper

10.1016/j.jalgebra.2006.11.042

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.

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