$A_\mathfrak{q}$-components of geometric classes in compact Hermitian locally symmetric spaces

DOI10.1215/21562261-2022-0031arXiv1812.03730MaRDI QIDQ6310950

Arghya Mondal

Publication date: 10 December 2018

Abstract: Let $$ be a compact Hermitian locally symmetric space, where $G$ is simple. We study the components of a de Rham cohomology class of $$, with respect to the Matsushima decomposition, where the class is obtained by taking Poincar'e dual of a totally geodesic complex analytic submanifold. Using an extension of the vanishing result of Kobayashi and Oda, we specify the existence of certain components of such cohomology classes when $G=extSU(p,q),5lepleq$.

Mathematics Subject Classification ID

Discrete subgroups of Lie groups (22E40) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67)

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