Group Representations on GL(2,F_q)

• Main Authors: Chiu-Lien Huang, 黃秀戀
• Other Authors: Liang-Chung Hsia
• Format: Others
• Language: en_US
• Published: 2002
• Online Access: http://ndltd.ncl.edu.tw/handle/99010384705937203359

碩士 === 國立中央大學 === 數學研究所 === 90 === This paper is a collation of all irreducible representations of GL(2, F_q). In order to do this, we need the basic knowledge about finite group representations. We arrange the basic understanding about finite group representations in §2. We state the basic results without proofs from Serre’s book on complex representations of finite groups [2]. For the proofs of all these results in §2, we refer to Serre’s book [2]. In §3, we start to find irreducible representations of GL(2, F_q). We use the projective line P(F_q) throught out the work. We can find q − 1 one-dimensional and q − 1 q-dimensional irreducible representations of GL(2, F_q). The part we refer to the paper[5] and Fulton’s book [7]. In §4, we use Frobenius method of induced representation which enables one to construct a representation of a group if a an irreducible representation of a subgroup is known. We use characters of Borel subgroup of GL(2, F_q) induces representations of GL(2, F_q). In §5, we bring in Cuspidal representation of GL(2, F_q). We can construct other irreducible representations of GL(2, F_q) by using cuspidal representation.