Construction of cohomology of discrete groups

Tong, Y. L.; Wang, S. P.

doi:10.1090/S0002-9947-1988-0933315-8

Construction of cohomology of discrete groups
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by Y. L. Tong and S. P. Wang

Trans. Amer. Math. Soc. 306 (1988), 735-763

DOI: https://doi.org/10.1090/S0002-9947-1988-0933315-8

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Abstract:

A correspondence between Hermitian modular forms and vector valued harmonic forms in locally symmetric spaces associated to $U(p, q)$ is constructed and also shown in general to be nonzero. The construction utilizes Rallis-Schiffmann type theta functions and simplified arguments to circumvent differential geometric calculations used previously in related problems.

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