Unipotent Representations, Theta Correspondences, and Quantum Induction

IF 2 4区数学 Q1 MATHEMATICS Memoirs of the American Mathematical Society Pub Date : 2024-07-01 DOI:10.1090/memo/1496

Hongyu He

引用次数: 0

Abstract

In this paper, we construct unipotent representations for the real orthagonal groups and the metaplectic groups in the sense of Vogan. Our construction is based on quantum induction which involves the compositions of even number of theta correspondences. In particular, our results imply that there are irreducible unitary representations attached to each special nilpotent orbit.

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单能表示、Theta 对应和量子归纳

在本文中，我们构建了实正交群和 Vogan 意义上的元映射群的单能表示。我们的构造基于量子归纳法，其中涉及偶数 Theta 对应的组合。特别是，我们的结果意味着每个特殊零potent 轨道都有不可还原的单元表示。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Memoirs of the American Mathematical Society 数学-数学

CiteScore

3.50

自引率

5.30%

发文量

审稿时长

>12 weeks

期刊介绍： Memoirs of the American Mathematical Society is devoted to the publication of research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers or groups of cognate papers in book form, and is under the supervision of the Editorial Committee of the AMS journal Transactions of the AMS. To be accepted by the editorial board, manuscripts must be correct, new, and significant. Further, they must be well written and of interest to a substantial number of mathematicians.

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