关于幂偶群的Howe结果的推广

IF 0.9 3区数学 Q2 MATHEMATICS, APPLIED

Bulletin des Sciences Mathematiques Pub Date : 2024-11-14 DOI:10.1016/j.bulsci.2024.103536

Souha Maaref

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引用次数: 0

摘要

设F是特征为零的非阿基米德局部域，G是定义在F上的一个单幂代数群，G的有理点的集合用G表示，是一个p进李群。设g是g的李代数，设H是g的正规闭子群，χ是H的酉特征，π是g在Hilbert空间Hπ中的不可约酉表示。本文的目的是确定π的χ-半不变向量所构成的空间。

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On a generalization of a result of Howe for unipotent groups

Let F be a nonarchimedean local field of characteristic zero and G be a unipotent algebraic group defined over F. The set of rational points of G, denoted by G, is a p-adic Lie group. Let

g

be the Lie algebra of G. Now let H be a normal closed subgroup of G, χ be a unitary character of H and π be an irreducible unitary representation of G in a Hilbert space