The character theory of finite groups of Lie type : a guided tour /
Meinolf Geck, Gunter Malle.
Bok Engelsk 2020 · Electronic books.
| Annen tittel | |
|---|---|
| Medvirkende | Malle, Gunter, (author.)
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| Utgitt | Cambridge University Press
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| Omfang | 1 online resource (ix, 394 pages) : : digital, PDF file(s).
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| Opplysninger | Title from publisher's bibliographic system (viewed on 20 Feb 2020).. - Cover -- Half-title -- Series information -- Title page -- Copyright information -- Contents -- Preface -- 1 Reductive Groups and Steinberg Maps -- 1.1 Affine Varieties and Algebraic Groups -- 1.2 Root Data -- 1.3 Chevalley's Classification Theorems -- 1.4 Frobenius Maps and Steinberg Maps -- 1.5 Working with Isogenies and Root Data -- Examples -- 1.6 Generic Finite Reductive Groups -- 1.7 Regular Embeddings -- 2 Lusztig's Classification of Irreducible Characters -- 2.1 Generalities about Character Tables -- 2.2 The Virtual Characters of Deligne and Lusztig -- 2.3 Unipotent Characters and Degree Polynomials -- 2.4 Towards Lusztig's Main Theorem 4.23 -- 2.5 Geometric Conjugacy and the Dual Group -- 2.6 The Jordan Decomposition of Characters -- 2.7 Average Values and Unipotent Support -- 2.8 On the Values of Green Functions -- 3 Harish-Chandra Theories -- 3.1 Harish-Chandra Theory for BN-Pairs -- 3.2 Harish-Chandra Theory for Groups of Lie Type -- 3.3 Lusztig Induction and Restriction -- 3.4 Duality and the Steinberg Character -- 3.5 d-Harish-Chandra Theories -- 4 Unipotent Characters -- 4.1 Characters of Weyl Groups -- 4.2 Families of Unipotent Characters and Fourier Matrices -- 4.3 Unipotent Characters in Type A -- 4.4 Unipotent Characters in Classical Types -- 4.5 Unipotent Characters in Exceptional Types -- 4.6 Decomposition of R[sup(G)sub(L)] and d-Harish-Chandra Series -- 4.7 On Lusztig's Jordan Decomposition -- 4.8 Disconnected Groups, Groups with Disconnected Centre -- Appendix Further Reading and Open Questions -- References -- Index.. - 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.
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| Emner | |
| Sjanger | |
| Dewey | |
| ISBN | 1-108-77908-5
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