单位三角形群的性质与Mackey方法

IF 0.8 4区数学 Q2 MATHEMATICS

Expositiones Mathematicae Pub Date : 2025-01-23 DOI:10.1016/j.exmath.2025.125656

Mikhail Ignatev , Mikhail Venchakov

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引用次数: 0

摘要

设U是有限域上的幺三角形群。我们考虑一类有趣的U的不可约复字符，即深度为2的字符。这是继极大维和次极大维特征之后的一个自然步骤，它们的描述已经已知。我们用定义代数方程系统明确地描述了深度为2的特征的支持。然后，计算支持元素上这样一个字符的值。证明中使用的主要技术工具是半直接积的麦基小群法。

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Characters of the unitriangular group and the Mackey method

Let

U

be the unitriangular group over a finite field. We consider an interesting class of irreducible complex characters of

U

, so-called characters of depth 2. This is a next natural step after characters of maximal and submaximal dimension, whose description is already known. We explicitly describe the support of a character of depth 2 by a system of defining algebraic equations. After that, we calculate the value of such a character on an element from the support. The main technical tool used in the proofs is the Mackey little group method for semidirect products.

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来源期刊

Expositiones Mathematicae 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

40 days

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