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研究生： 王義榮
Wang, Yi-Rong
論文名稱： SL(3,q)及其子群的特徵表應用
An application of character tables of SL(3,q) and its subgroups
指導教授： 黃世昌
Huang, Shih-Chang
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系應用數學碩博士班
Department of Mathematics
論文出版年： 2013
畢業學年度： 101
語文別： 英文
論文頁數： 95
中文關鍵詞： 共軛類 、特徵表 、Dade猜想
外文關鍵詞： conjugacy class, character table
相關次數： 點閱：196  下載：4 
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    • 在這篇論文裡，我們完整的找出SL(3,q)的共軛類，並將SL(3,q)及其子群的特徵表完成。除此之外，將特徵表應用在證明Dade猜想。

    In this thesis, the conjugacy classes of SL(3,q) will be determined completely. We also determine the character tables of SL(3,q) and its parabolic subgroups. As an application, we apply these character tables to verify Dade's conjecture.

    0 List of Notation ...8 1 Introduction ...11 2 Elementary Theories of Representations and Characters ...15 2.1 Preliminaries ...15 2.2 Lifting of Characters and Induction of Characters ...19 3 Structure of SL(3,q) ...21 3.1 Conjugacy Classes of SL(3,q) ...21 3.2 Regular Semisimple Classes and Primary Classes ...30 4 Characters of SL(3,q) and its parabolic subgroups ...32 4.1 Irreducible Characters of Borel subgroup ...32 4.2 Irreducible Characters of maximal parabolic subgroups ...39 4.3 Irreducible Characters of SL(3,q) ...44 5 Dade's conjecture for SL(3,q) ...61 5.1 Introduction of Dade's Conjecture ...61 5.2 The p-Block of SL(3,q) ...63 5.3 Dade's ordinary conjecture for SL(3,q) ...71 5.4 Dade's invariant conjecture for SL(3,q) ...74 5.4.1 Lemmas from elementary number theory ...74 5.4.2 Action of Automorphisms on Irreducible Characters ...75 5.4.3 Verify the Dade Invariant Conjecture for SL(3,q) ...79 Appendices ...81 A Table ...82 B Dade's Conjecture ...91 Bibliography ...93 Index ...95

    [1] Results on Dade's conjecture, 2010, http://www.math.ncku.edu.tw/~shuang/Dade_uptodate.pdf.
    [2] Ayoub Basheer, Character Table of the General Linear Group and Some of its Subgroups, (2008).
    [3] A. et al. Borel, Seminar on algebraic groups and related finite group, Lecture Notes in Math. 131 (1970).
    [4] N. Burgoyne and C. Williamson, On a theorem of Borel and Tits for finite Chevalley groups, Arch. Math. 27 (1976), 489-491.
    [5] E. C. Dade, Counting characters in blocks, I, Invent. math. 109 (1992), 187-210.
    [6] E. C. Dade, Counting characters in blocks, II, J. Reine Angew. Math. 448 (1994),97-190.
    [7] E. C. Dade, Counting characters in blocks, II.9, In: Solomon, R., ed. Representation Theory of Finite Groups (1997), 45-59.
    [8] H. Enomoto and H. Yamada, The characters of G_2(2^n), Japan. J. Math 12 (1986),325-377.
    [9] J. A. Green, The characters of the _nite general linear groups, Trans. Amer. Math. Soc 80 (1956), 402-447.
    [10] J. A. Green, Discrete series characters for GL(n,q), algebras and representation theory2, (1999), 61-82.
    [11] G. James and M. Liebeck, Representations and characters of groups, 2 ed., 2001.
    [12] I. Janiszczak, P. Fleischmann, and R. Knorr, The number of regular semisimple classes of special linear and unitary groups, Linear Algebra Appl. 274 (1998),17-26.
    [13] R. Knorr and G. Robinson, Some remarks on a conjecture of Alperin., J. London Math. Soc. (2) 39 (1989), 48-60.
    [14] M. L. Lewis, M. Bianchi, D. Chillag, and E. Pacifici, Character degree graphs that are complete graphs, Proc. Amer. Math 135 (2007), 671-676.

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