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arXiv · 2312.13073

Full theta lifting for type II reductive dual pairs

Huajian Xue
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Abstract

In this article, we study the full theta lifting for two cases of type II reductive dual pairs over a nonarchimedean local field. Firstly, we determine the structure of the full theta lifts of all irreducible representations for dual pair $(\mathrm{GL}(2),\mathrm{GL}(2))$. Secondly, we prove that the full theta lift of an irreducible tempered representation is irreducible and tempered for dual pair $(\mathrm{GL}(n),\mathrm{GL}(n+1))$, where $n$ is a positive integer.

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BibTeXRIS

Huajian Xue. 2023-12-20. Full theta lifting for type II reductive dual pairs. https://arxiv.org/abs/2312.13073

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