The Frobenius Characteristic of Character Polynomials

IF 1.8 4区综合性期刊 Q2 MULTIDISCIPLINARY SCIENCES

Journal of the Indian Institute of Science Pub Date : 2022-09-26 DOI:10.1007/s41745-022-00327-8

Amritanshu Prasad

引用次数: 1

Abstract

Polynomials in an infinite sequence of variables can be evaluated as class functions of symmetric groups on \(n\) letters across all \(n\). When they represent characters of families of representations, they are called character polynomials. This article is an introduction to the theory of character polynomials and their Frobenius characteristics. As an application, some generating functions describing the restriction of a polynomial representation of \(GL_n\) to \(S_n\) are obtained.

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特征多项式的Frobenius特征

无穷变量序列中的多项式可以作为横跨所有\(n\)的\(n\)字母上对称群的类函数来计算。当它们表示表示族的特征时，它们被称为特征多项式。本文介绍了特征多项式的理论及其Frobenius特征。作为应用，得到了一些描述\(GL_n\)的多项式表示对\(S_n\)的限制的生成函数。

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

Journal of the Indian Institute of Science MULTIDISCIPLINARY SCIENCES-

CiteScore

4.30

自引率

0.00%

发文量

期刊介绍： Started in 1914 as the second scientific journal to be published from India, the Journal of the Indian Institute of Science became a multidisciplinary reviews journal covering all disciplines of science, engineering and technology in 2007. Since then each issue is devoted to a specific topic of contemporary research interest and guest-edited by eminent researchers. Authors selected by the Guest Editor(s) and/or the Editorial Board are invited to submit their review articles; each issue is expected to serve as a state-of-the-art review of a topic from multiple viewpoints.