Representations of Gl 2 (f Q )
نویسنده
چکیده
In order to explore Representation Theory as a logical follow-up to group theory, I attempt to enumerate the irreducible representations of GL2(Fq). In order to do so, I first introduce the idea of a representation and provide a simple example. Next, I prove the existance of an irreducible decomposition for a given representation and introduce a useful result of characters. Finally, four types of the representations desired are shown to completely describe all irreducible representations of GL2(Fq).
منابع مشابه
M ay 2 00 8 Admissible unitary completions of locally Q p - rational representations of GL 2 ( F )
Let F be a finite extension of Q p , p > 2. We construct admissible unitary completions of certain representations of GL 2 (F) on L-vector spaces, where L is a finite extension of F. When F = Q p using the results of Berger, Breuil and Colmez we obtain some results about lifting 2-dimensional mod p representations of the absolute Galois group of Q p to crystabelline representations with given H...
متن کاملOctahedral Galois Representations Arising from Q-curves of Degree 2
Generically, one can attach to a Q-curve C octahedral representations ρ : Gal(Q/Q) −→ GL 2 (F 3) coming from the Galois action on the 3-torsion of those abelian varieties of GL 2-type whose building block is C. When C is defined over a quadratic field and has an isogeny of degree 2 to its Galois conjugate, there exist such representations ρ having image into GL 2 (F 9). Going the other way, we ...
متن کاملGlobally analytic $p$-adic representations of the pro--$p$--Iwahori subgroup of $GL(2)$ and base change, I : Iwasawa algebras and a base change map
This paper extends to the pro-$p$ Iwahori subgroup of $GL(2)$ over an unramified finite extension of $mathbb{Q}_p$ the presentation of the Iwasawa algebra obtained earlier by the author for the congruence subgroup of level one of $SL(2, mathbb{Z}_p)$. It then describes a natural base change map between the Iwasawa algebras or more correctly, as it turns out, between the global distribut...
متن کاملm at h . Q A ] 1 9 O ct 1 99 9 Actions of GL q ( 2 , C ) on C ( 1 , 3 ) and its four dimensional representations
Actions of GL q (2, C) on C(1, 3) and its four dimensional representations Abstract. A complete classification is given of all inner actions on the Clif-ford algebra C(1, 3) defined by representations of the quantum group GL q (2, C), q m = 1 with nonzero perturbations. As a consequence of this classification it is shown that the space of invariants of every GL q (2, C)-action of this type, whi...
متن کاملJ an 2 00 9 TENSOR PRODUCTS OF IRREDUCIBLE REPRESENTATIONS OF THE GROUP GL ( 3 , F q )
We describe the tensor products of two irreducible linear complex representations of the group G = GL(3, Fq) in terms of induced representations by linear characters of maximal torii and also in terms of classical and generalized Gelfand-Graev representations. Our results include MacDonald’s conjectures for G and at the same time they are extensions to G of finite counterparts to classical resu...
متن کاملIncidence Homology of Finite Projective Spaces
Let F be the finite field of q elements and let P(n, q) be the projective space of dimension n−1 over F. We construct a family H k,i of combinatorial homology modules associated to P(n, q) over a coefficient field F field of characteristic p0 > 0 co-prime to q. As FGL(n, q) -representations the modules are obtained from the permutation action of GL(n, q) on the subspaces of F. We prove a branch...
متن کامل