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研究生： 俞若婷
Yu, Alison
論文名稱： GL_2(F_q) 與 GL_3(F_q) 的 Deligne-Lusztig 虛擬特徵
Deligne-Lusztig virtual characters of GL_2(F_q) and GL_3(F_q)
指導教授： 潘戍衍
Pan, Shu-Yen
口試委員: 鄭志豪
楊一帆
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系
Department of Mathematics
論文出版年： 2013
畢業學年度： 101
語文別： 英文
論文頁數： 41
中文關鍵詞： 群表現
外文關鍵詞： character, Deligne-Lusztig, GL_2(F_q), GL_3(F_q)
相關次數： 點閱：38  下載：0 
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    • The general method to find irreducible representations of GL2(Fq) and GL3(Fq) is using induction from Borel subgroup B or parabolic subgroup P.
    But there exists some irreducible characters which are not easy to find.
    We have to compose such characters with not obvious way.
    Deligne-Lusztig give us better method to find irreducible characters of GL2(Fq) and GL3(Fq) by virtual characters RGT\theta for a pair of a maximal torus T and a character \theta of T.
    In this thesis we work out all Deligne-Lusztig virtual characters of GL2(Fq) and GL3(Fq).

    The general method to find irreducible representations of GL2(Fq) and GL3(Fq) is using induction from Borel subgroup B or parabolic subgroup P.
    But there exists some irreducible characters which are not easy to find.
    We have to compose such characters with not obvious way.
    Deligne-Lusztig give us better method to find irreducible characters of GL2(Fq) and GL3(Fq) by virtual characters RGT\theta for a pair of a maximal torus T and a character \theta of T.
    In this thesis we work out all Deligne-Lusztig virtual characters of GL2(Fq) and GL3(Fq).

    Chapter 1. Introduction 1. Definition of representations 2. Characters 3. Induced representations and character of a induced representation 4. Introduction to Deligne-Lusztig virtual characters Chapter 2. The characters of GL_2(F_q) 1. Some subgroups of GL_2(F_q) and the order of GL_2(F_q) 2. The conjugacy classes in GL_2(F_q) 3. The irreducible representations of GL_2(F_q) Chapter 3. The characters of GL_3(F_q) 1. The order of GL_3(F_q) 2. The conjugacy classes in GL_2(F_q) 3. The irreducible representations of GL_2(F_q) Chapter 4. Deligne-Lusztig virtual characters 1. GL_2(F_q) 2. GL_3(F_q) Bibliography

    [1]R. W. Carter, Finite Groups of Lie Type, Wiley-Interscience, New York, 1985.
    [2]F. Digne and J. Michel, Representations of Finite Group of Lie Type, Cambridge University, Great Britain, 1991.
    [3]W. Fulton and J. Harris, Representation Theory : A First Course, Springer-Verlag, New York, 1991.
    [4]J. E. Humphreys, Linear Algebraic Groups, Springer-Verlag, New York, 1975.
    [5]J.-P. Serre, Linear Representations of Finite Groups, Springer-Verlag, New York, 1977.
    [6]R. Steinberg, The representations of GL(3,q), GL(4,q), PGL(3,q), PGL(4,q), Canadian Journal of Mathematics, Vol. 3, 1951, 225--235.

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