《The Modular Atlas Project(Hiss)》.pdf

The Main Goals Computational Methods The 2-Modular Character Table of the Fischer Group Fi23 The Modular Atlas Project Gerhard Hiss Lehrstuhl D für Mathematik RWTH Aachen Lehrstuhl D für Mathematik RWTH Aachen 6th Symposium on Algebra and Computation Tokyo, 15.–18.11.2005 Gerhard Hiss The Modular Atlas Project The Main Goals Classification of Representations Computational Methods Character Tables The 2-Modular Character Table of the Fischer Group Fi23 The Modular Atlas Representations Let G be a finite group and F a field. An F-representation of G of degree d is a homomorphism X : G → GL( V), where V is a d-dimensional F-vector space. Choosing a basis of V, we obtain a matrix representation G → GLd (F) to compute with. X is irreducible, if V does not have any proper G-invariant subspaces. Gerhard Hiss The Modular Atlas Project The Main Goals Classification of Representations Computational Methods Character Tables The 2-Modular Character Table of the Fischer Group Fi23 The Modular Atlas Classification Fact There are only finitely many irreducible F-representations of G up to equivalence. Aims Classify all irreducible representations for a given group G and a given field F . Describe all irreducible representations of all finite simple groups. Use a computer for sporadic simple groups. Gerhard Hi