A generalized Cartan decomposition for the double coset space
نویسنده
چکیده
Motivated by recent developments on visible actions on complex manifolds, we raise a question whether or not the multiplication of three subgroups L, G and H surjects a Lie group G in the setting that G/H carries a complex structure and contains G/G ∩ H as a totally real submanifold. Particularly important cases are when G/L and G/H are generalized flag varieties, and we classify pairs of Levi subgroups (L,H) such that LGH = G, or equivalently, the real generalized flag variety G/H ∩ G meets every L-orbit on the complex generalized flag variety G/H in the setting that (G,G) = (U(n), O(n)). For such pairs (L,H), we introduce a herringbone stitch method to find a generalized Cartan decomposition for the double coset space L\G/H, for which there has been no general theory in the non-symmetric case. Our geometric results provides a unified proof of various multiplicity-free theorems in representation theory of general linear groups. ∗Partly supported by Grant-in-Aid for Exploratory Research 16654014, Japan Society of the Promotion of Science
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تاریخ انتشار 2006