Finite Groups of Lie Type: Conjugacy Classes and Complex Characters
The finite groups of Lie type are of basic importance in the theory of groups. A classic in its field, this book presents the theories of finite groups of Lie type in a clear and accessible style, especially with regard to the main concepts of the theory and the techniques of proof used, and gives a detailed exposition of the complex representation theory.
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Introduction to Algebraic Groups
BVPairs and Coxeter Groups
Maximal Tori and Semisimple Classes
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adic cohomology adjoint affine variety algebraic variety automorphism bijective BN-pair Borel subgroup CG(s characteristic characters of GF conjugacy classes conjugate connected reductive group consider Coxeter group cuspidal characters cuspidal unipotent characters decomposition define degree double coset Dynkin diagram eigenvalues element of G F-stable maximal torus finite group follows Frobenius map G-orbit geometric conjugacy class given group G Hence homomorphism induced integer irreducible characters irreducible components isomorphic Lemma Let G Levi subgroup Lie algebra lies Lusztig Moreover morphism multiplication nilpotent orbits nonzero obtain open subset pairs parabolic subgroup partitions polynomial Proof Proposition Qp/Z regular unipotent elements representation result root subgroups root system satisfies semisimple element sheaf simple roots subalgebra subgroup of G Suppose surjective symbol theorem tori torus of G unipotent classes unipotent elements unique vector Weyl group