ON EXTERIOR POWERS OF REFLECTION REPRESENTATIONS

IF 0.6 4区数学 Q3 MATHEMATICS

Bulletin of the Australian Mathematical Society Pub Date : 2023-10-06 DOI:10.1017/s0004972723000965

HONGSHENG HU

引用次数: 0

Abstract

Abstract In 1968, Steinberg [ Endomorphisms of Linear Algebraic Groups , Memoirs of the American Mathematical Society, 80 (American Mathematical Society, Providence, RI, 1968)] proved a theorem stating that the exterior powers of an irreducible reflection representation of a Euclidean reflection group are again irreducible and pairwise nonisomorphic. We extend this result to a more general context where the inner product invariant under the group action may not necessarily exist.

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论反射表征的外部幂

1968年，Steinberg[线性代数群的自同态，Memoirs of the American Mathematical Society, 1980]证明了欧氏反射群的不可约反射表示的外幂也是不可约且对非同构的定理。我们将这一结果推广到群作用下的内积不变量不一定存在的更一般的情况。

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

Bulletin of the Australian Mathematical Society 数学-数学

CiteScore

1.20

自引率

14.30%

发文量

149

审稿时长

4-8 weeks

期刊介绍： Bulletin of the Australian Mathematical Society aims at quick publication of original research in all branches of mathematics. Papers are accepted only after peer review but editorial decisions on acceptance or otherwise are taken quickly, normally within a month of receipt of the paper. The Bulletin concentrates on presenting new and interesting results in a clear and attractive way. Published Bi-monthly Published for the Australian Mathematical Society