A vanishing theorem for modular symbols on locally symmetric spaces |
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Authors: | T. Kobayashi T. Oda |
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Affiliation: | (1) Graduate School of Mathematical Sciences, University of Tokyo, Meguro, Komaba, 153, Tokyo, Japan , JP |
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Abstract: | A modular symbol is the fundamental class of a totally geodesic submanifold embedded in a locally Riemannian symmetric space , which is defined by a subsymmetric space . In this paper, we consider the modular symbol defined by a semisimple symmetric pair (G,G'), and prove a vanishing theorem with respect to the -component in the Matsushima-Murakami formula based on the discretely decomposable theorem of the restriction . In particular, we determine explicitly the middle Hodge components of certain totally real modular symbols on the locally Hermitian symmetric spaces of type IV. Received: December 8, 1996 |
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Keywords: | . Modular symbols semisimple Lie group Zuckerman-Vogan module Matsushima-Murakami formula modular varieties discrete decomposable restriction bounded symmetric domain discontinuous group symmetric space. |
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