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arXiv 0907.4605math.GRmath.RT
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有限Coxeter群的Gelfand模型

On Gelfand models for finite Coxeter groups

Shripad M. Garge, Joseph Oesterle

摘要:

有限群$G$的Gelfand模型是$G$的复线性表示,它包含它的每个重数为1的不可约表示。对于具有忠实表示$V$的有限群$G$,构造一个表示,我们称之为与$V$相关联的$G$的多项式模型。Araujo等人证明了某些不可约外尔群的多项式模型与它们的规范表示相关联是Gelfand模型。本文给出了一般有限Coxeter群的多项式模型及其标准表示的一个较简单而统一的研究方法。我们的最终结果是有限Coxeter群$G$的多项式模型是Gelfand模型当且仅当$G$没有$W(D_{2n}), W(E_7)$或$W(E_8)$类型的直因子。

英文摘要:

A Gelfand model for a finite group $G$ is a complex linear representation of $G$ that contains each of its irreducible representations with multiplicity one. For a finite group $G$ with a faithful representation $V$, one constructs a representation which we call the polynomial model for $G$ associated to $V$. Araujo and others have proved that the polynomial models for certain irreducible Weyl groups associated to their canonical representations are Gelfand models. In this paper, we give an easier and uniform treatment for the study of the polynomial model for a general finite Coxeter group associated to its canonical representation. Our final result is that such a polynomial model for a finite Coxeter group $G$ is a Gelfand model if and only if $G$ has no direct factor of the type $W(D_{2n}), W(E_7)$ or $W(E_8)$.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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