Locally symmetric spaces and the cohomology of the Weil representation
| dc.contributor.advisor | Millson, John | en_US |
| dc.contributor.author | Shi, Yousheng | en_US |
| dc.contributor.department | Mathematics | en_US |
| dc.contributor.publisher | Digital Repository at the University of Maryland | en_US |
| dc.contributor.publisher | University of Maryland (College Park, Md.) | en_US |
| dc.date.accessioned | 2019-09-27T05:37:38Z | |
| dc.date.available | 2019-09-27T05:37:38Z | |
| dc.date.issued | 2019 | en_US |
| dc.description.abstract | We study generalized special cycles on Hermitian locally symmetric spaces $\Gamma \backslash D$ associated to the groups $G=\mathrm{U}(p,q)$, $\mathrm{Sp}(2n,\R) $ and $\mathrm{O}^*(2n) $. These cycles are covered by symmetric spaces associated to subgroups of $G$ which are of the same type. Using the oscillator representation and the thesis of Greg Anderson (\cite{Anderson}), we show that Poincar\'e duals of these generalized special cycles can be viewed as Fourier coefficients of a theta series. This gives new cases of theta lifts from the cohomology of Hermitian locally symmetric manifolds associated to $G $ to vector-valued automorphic functions associated to the groups $G'=\mathrm{U}(m,m)$, $\mathrm{O}(m,m)$ or $\mathrm{Sp}(m,m)$ which are members of a dual pair with $G$ in the sense of Howe. The above three groups are all the groups that show up in real reductive dual pairs of type I whose symmetric spaces are of Hermitian type with the exception of $\mathrm{O}(p,2)$. | en_US |
| dc.identifier | https://doi.org/10.13016/vk0e-xd1q | |
| dc.identifier.uri | http://hdl.handle.net/1903/25018 | |
| dc.language.iso | en | en_US |
| dc.subject.pqcontrolled | Mathematics | en_US |
| dc.subject.pquncontrolled | cohomology | en_US |
| dc.subject.pquncontrolled | generalized special cycles | en_US |
| dc.subject.pquncontrolled | Hermitian locally symmetric spaces | en_US |
| dc.subject.pquncontrolled | Poincare dual | en_US |
| dc.subject.pquncontrolled | theta correspondence | en_US |
| dc.subject.pquncontrolled | Weil representation | en_US |
| dc.title | Locally symmetric spaces and the cohomology of the Weil representation | en_US |
| dc.type | Dissertation | en_US |
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