一元$\rm{SL}_2(\mathbb{R})$表示的分类注释

Q3 Mathematics

International Journal of Mathematics in Operational Research Pub Date : 2023-10-16 DOI:10.5539/jmr.v15n5p22

Amjad Alghamdi

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引用次数: 0

摘要

本文的目的是用归纳表示技术解释Gelfand所做的幺正SL_2(R)表示的分类。从子群n中导出了SL_2(R)表示，得到了在二元齐次函数空间上构造的一个表示。然后，我们逐步归纳出SL_2(R)的表示。因此，SL_2(R)的表示作用于一个一元函数空间。

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Note on the Classification of the Unitary $\rm{SL}_2(\mathbb{R})$ Representations

The aim of this paper is to explain the classification of the unitary SL_2(R) representations done by Gelfand by using the induced representation technique. We induce the SL_2(R) representation from the subgroup N. We get a representation constructed on a space of homogeneous functions in two variables. Then, we move to induce the SL_2(R) representation in stages. Consequently, the representation of SL_2(R) acts on a space of functions of one variable.

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来源期刊

International Journal of Mathematics in Operational Research Decision Sciences-Decision Sciences (all)

CiteScore

2.10

自引率

0.00%

发文量