Tight Homomorphisms and Hermitian Symmetric Spaces
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We introduce the notion of tight homomorphism into a locally compact group with nonvanishing bounded cohomology and study these homomorphisms in detail when the target is a Lie group of Hermitian type. Tight homomorphisms between Lie groups of Hermitian type give rise to tight totally geodesic maps of Hermitian symmetric spaces. We show that tight maps behave in a functorial way with respect to the Shilov boundary and use this to prove a general structure theorem for tight homomorphisms. Furthermore, we classify all tight embeddings of the Poincaré disk.
Keywords and phrasesHermitian symmetric spaces bounded cohomology Shilov boundary totally geodesic embedding tight homomorphism
2000 Mathematics Subject Classification53C24 53C35 32M15
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