Lectures on Chevalley Groups, Parts 1-4 |
Contents
Page | 7 |
Central extensions | 73 |
The orders of the finite Chevalley groups | 130 |
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Abelian adjoint algebraic group algebraically closed Assume basis center of G central extension Chevalley group choose coefficients commutes conjugate Corollary corresponding defined denote diagonal double cosets elements equation Exercise exists finite field fixed follows G is universal G₂ group G Hence highest weight homomorphism indecomposable induction integral invariant isomorphism KG-module lattice Lemma Let G LIBRARIES STANFORD UNIVERSITY Lie algebra Lie group linear matrices maximal minimal expression multiplication nonzero normal subgroup orthogonal permutation polynomial positive roots proof of Theorem prove relations Remark representation result root system semisimple simple roots STANFORD UNIVERSITY LIBRARIES subgroup of G subset superdiagonal Theorem 28 unipotent UNIVERSITY LIBRARIES STANFORD V₁ W₁ weight vector Weyl group whence write α α α β π π