ISSN:
1420-8946
Keywords:
Key words. Modular symbols, semisimple Lie group, Zuckerman-Vogan module, Matsushima-Murakami formula, modular varieties, discrete decomposable restriction, bounded symmetric domain, discontinuous group, symmetric space.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract. A modular symbol is the fundamental class of a totally geodesic submanifold $ \Gamma'\backslash G'/K' $ embedded in a locally Riemannian symmetric space $ \Gamma \backslash G / K $ , which is defined by a subsymmetric space $ G'/ K' \hookrightarrow G / K $ . 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 $ \pi $ -component $ (\pi \in \widehat {G}) $ in the Matsushima-Murakami formula based on the discretely decomposable theorem of the restriction $ \pi |_{G'} $ . In particular, we determine explicitly the middle Hodge components of certain totally real modular symbols on the locally Hermitian symmetric spaces of type IV.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s000140050045
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