Orbit Correspondences for Real Reductive Dual Pairs
نویسندگان
چکیده
Suppose that V ,W be a symplectic space and a quadratic space respectively over R. Let g1,g2 be the Lie algebras of the groups of isometries of two spaces. Let τi :V ⊗RW → gi be the moment maps and O be the closure of a nilpotent orbit O in gi for i = 1 or 2. In this paper we show that τ3−i (τ −1 i (O )) is a union of at most two closures of nilpotent orbits in g3−i .
منابع مشابه
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Theta correspondence y over R is established by Howe (J. Amer. Math. Soc. 2 (1989) 535). In He (J. Funct. Anal. 199 (2003) 92), we prove that y preserves unitarity under certain restrictions, generalizing the result of Li (Invent. Math. 97 (1989) 237). The goal of this paper is to elucidate the idea of constructing unitary representation through the propagation of theta correspondences. We show...
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