The Character Theory of Finite Groups of Lie Type
The Character Theory of Finite Groups of Lie Type
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DOI：
10.1017/9781108779081
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发表时间：
2020-02
期刊：
影响因子：
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通讯作者：
M. Geck;G. Malle
中科院分区：
文献类型：
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作者：
M. Geck;G. Malle
通过 Deligne 和 Lusztig 在 20 世纪 70 年代的基础工作，并主要由 Lusztig 进一步发展，有限域上的约简群特征理论已经发展成为一个丰富而广阔的数学领域。它结合了代数几何、拓扑、组合学和计算机代数的工具和方法，并且自此有了很大的发展。通过这本书，作者满足了当代治疗的需要，在核心领域补充了卡特和迪涅-米歇尔的成熟书籍。作者专注于有限群理论中的应用，收集了以前分散的结果，让读者能够掌握有关该主题的大量文献，涵盖的主题包括正则嵌入、字符的 Jordan 分解、d-Harish-Chandra 理论和单能字符的 Lusztig 归纳等。这本有用的参考书只需要一定的代数几何背景，适合研究生和研究人员。
Through the fundamental work of Deligne and Lusztig in the 1970s, further developed mainly by Lusztig, the character theory of reductive groups over finite fields has grown into a rich and vast area of mathematics. It incorporates tools and methods from algebraic geometry, topology, combinatorics and computer algebra, and has since evolved substantially. With this book, the authors meet the need for a contemporary treatment, complementing in core areas the well-established books of Carter and Digne–Michel. Focusing on applications in finite group theory, the authors gather previously scattered results and allow the reader to get to grips with the large body of literature available on the subject, covering topics such as regular embeddings, the Jordan decomposition of characters, d-Harish–Chandra theory and Lusztig induction for unipotent characters. Requiring only a modest background in algebraic geometry, this useful reference is suitable for beginning graduate students as well as researchers.