A remark on the orbit structure of the complexification of a semisimple symmetric space |
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Authors: | Laura Geatti |
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Institution: | Dipartimento di Matematica, Università di Roma 2 Tor Vergata, 00133 Roma, Italy |
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Abstract: | We consider the action of a real semisimple Lie group G on the complexification of a semisimple symmetric space and we present a refinement of Matsuki?s results (Matsuki, 1997 1]) in this case. We exhibit a finite set of points in , sitting on closed G-orbits of locally minimal dimension, whose slice representation determines the G-orbit structure of . Every such point lies on a compact torus and occurs at specific values of the restricted roots of the symmetric pair . The slice representation at is equivalent to the isotropy representation of a real reductive symmetric space, namely . In principle, this gives the possibility to explicitly parametrize all G-orbits in . |
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