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Main Authors: Haan, Jaeho, Kwon, Sanghoon
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2410.02625
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author Haan, Jaeho
Kwon, Sanghoon
author_facet Haan, Jaeho
Kwon, Sanghoon
contents In this paper, we examine the tower property concerning the genericity of global theta lifts between various classical groups, drawing inspiration from Rallis' tower property. By exploring the relationship between the analytic properties of $L$-functions and special Bessel and Fourier-Jacobi periods, we demonstrate that the first occurrence of global theta lifts between dual reductive groups preserves genericity. As an application, we establish the global Gan-Gross-Prasad conjecture for $\SO_{2n+1} \times \SO_{2}$ under the assumption that $\SO_{2}$ is split and its representation is trivial.
format Preprint
id arxiv_https___arxiv_org_abs_2410_02625
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle The tower property on the genericity of global theta lifts
Haan, Jaeho
Kwon, Sanghoon
Number Theory
Representation Theory
In this paper, we examine the tower property concerning the genericity of global theta lifts between various classical groups, drawing inspiration from Rallis' tower property. By exploring the relationship between the analytic properties of $L$-functions and special Bessel and Fourier-Jacobi periods, we demonstrate that the first occurrence of global theta lifts between dual reductive groups preserves genericity. As an application, we establish the global Gan-Gross-Prasad conjecture for $\SO_{2n+1} \times \SO_{2}$ under the assumption that $\SO_{2}$ is split and its representation is trivial.
title The tower property on the genericity of global theta lifts
topic Number Theory
Representation Theory
url https://arxiv.org/abs/2410.02625