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研究生： 林瑞展
Lin, Rui-Chan
論文名稱： SU(3,q^2)的parabolic子群的特徵表應用
An application of character tables of parabolic subgroups of SU(3,q^2)
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： 96
中文關鍵詞： 特殊酉群 、有限群的特徵函數 、Dade猜想
外文關鍵詞： special unitary group, character of finite groups
相關次數： 點閱：213  下載：4 
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    • 特徵函數是由Frobenius在1896年提出的，這給了我們一個新的觀點去研究有限群。特徵函數表在群論中有很多應用。在這篇論文裡，我們先構造SU(3,q^2)的所有parabolic子群的特徵函數表，其中q是一個質數的任意次方。接著，我們運用這些結果來驗證表現理論上的一個有名猜想:Dade猜想。

    Character theory were defined by Frobenius in 1896. It give us a new viewpoint for finite group. There are many applications about character table in group theory. In this thesis, we construct the character tables of the parabolic subgroups of the special unitary group SU(3,q^2), q is a power of a prime p. Furthermore, we use these character tables to verify a famous conjecture formulated by Dade.

    0. Notation …………………………………………………………..8 1. Introduction ……………………………………………………..11 2. Preliminaries ……………………………………………………15 2.1 Some Definitions and Results from Character Theory ......15 3. Conjugacy Classes of SU(3,q^2) and its subgroups......19 3.1 Borel subgroup of SU(3,q^2)......19 3.2 Conjugacy Classes of SU(3,q^2)......22 3.3 Conjugacy Classes of Borel Subgroup......24 3.4 Conjugacy Classes of D......29 3.5 Regular Semisimple Classes and Primary Classes......32 4. Character Tables of SU(3,q^2) and its Borel subgroup......33 4.1 Irreducible Characters of B......33 4.2 Irreducible Characters of D with Degrees q and q-1......42 4.3 Irreducible Characters of SU(3,q^2)......46 5. Dade's Conjectures for SU(3,q^2)......67 5.1 Notation: radical p-chains, blocks of characters and the conjectures ......67 5.2 The p-block of SU(3,q^2)......71 5.2.1 Classify the p-blocks of SU(3,q^2) and its Borel subgroup......71 5.2.2 The induced block of p-block......76 5.3 Dade's Ordinary Conjecture for SU(3,q^2)......76 5.4 Dade's Invariant Conjecture for SU(3,q^2)......78 5.4.1 Lemmas from Elementary Number Theory......78 5.4.2 Action Of Automorphisms On Irreducible Character......79 5.4.3 Verify the Dade Invariant Conjecture......84 Appendices......86 A Table......87 Bibliography......93 Index......96

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