Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
121 tokens/sec
GPT-4o
9 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Symplectic models for Unitary groups (1611.01621v2)

Published 5 Nov 2016 in math.NT and math.RT

Abstract: In analogy with the study of representations of $GL_{2n}(F)$ distinguished by $Sp_{2n}(F)$, where $F$ is a local field, in this paper we study representations of $U_{2n}(F)$ distinguished by $Sp_{2n}(F)$. (Only quasi-split unitary groups are considered in this paper since they are the only ones which contain $Sp_{2n}(F)$.) We prove that there are no cuspidal representations of $U_{2n}(F)$ distinguished by $Sp_{2n}(F)$ for $F$ a non-archimedean local field. We also prove the corresponding global theorem that there are no cuspidal representations of $U_{2n}({\mathbb A}k)$ with nonzero period integral on $Sp{2n}(k) \backslash Sp_{2n}({\mathbb A}k)$ for $k$ any number field or a function field. We completely classify representations of quasi-split unitary group in four variables over local and global fields with nontrivial symplectic periods using methods of theta correspondence. We propose a conjectural answer for the classification of all representations of a quasi-split unitary group distinguished by $Sp{2n}(F)$.

Citations (10)

Summary

We haven't generated a summary for this paper yet.