博碩士論文 89221003 詳細資訊

 以作者查詢圖書館館藏 、以作者查詢臺灣博碩士 、以作者查詢全國書目 、勘誤回報 、線上人數：8 、訪客IP：34.204.168.209

(Group Representations on GL(2,F_q))

 ★ 數論在密碼學上的應用 ★ a^n-b^n的原質因子，其中a,b為高斯整數 ★ Legendre的定理在Z[i]和Z[w]的情形 ★ Diophantine approximation and the Markoff chain ★ The average of the number of r-periodic points over a quadratic number field. ★ 週期為r之週期點個數的平均值 ★ 橢圓曲線上扭點的平均數 ★ 正特徵值函數體上的逼近指數之研究 ★ On some problem in Arithmetic Dynamical System and Diophantine Approximation in Positive Characteristic ★ ZCm 的理想環生成元個數之上限

1. 本電子論文使用權限為同意立即開放。
2. 已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
3. 請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。

Serre’s book Complex Representations of Finite Groups。

Frobenius method of induced representation

Cuspidal representation。在這裡， 我們需要知道有關於cuspidal representation 的性質。

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.

★ GL(2
★ F_q)

2 Basic About Finite Group Representations
3 Irreducible Representations from Permutation Representation
4 Borel Subgroup
5 Cuspidal Representation

Fields, Contemporary Mathematics 16, American Mathematical Society, 1983.
[2] Jean-Pierre Serre, Linear Representations of Finite Groups, Springer-
Verlag, New York, 1977.
[3] J.L. Alpherin, Groups and Representations, Springer-Verlag, New York, 1995.
[4] Hua-Chien Li, A Note on Complex Representations of GL(2, F_q).
[5] Robert Steingerg The Representations of GL(2, F_q), GL(3, F_q), PGL(3, F_q),
And PGL(3, F_q), Canadian J. Math. 3, (1951), 225–235.
[6] Serge Lang, Algebra, Addison-Wesley Pub. Co., Advanced Book Program , 1984.
[7] William Fulton and Joe Harris , Representation Theory, Springer-Verlag,
1991.