Simple Groups of Lie Type |
Contents
The Classical Simple Groups | 1 |
Weyl Groups | 12 |
Simple Lie Algebras | 33 |
Copyright | |
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abstract Coxeter complex automorphism of G Cartan Cartan decomposition Cartan subalgebra chamber complex Chevalley basis Chevalley group co-roots coefficients commutator consider contains corresponding Coxeter element Coxeter group defined denote double coset Dynkin diagram eigenvalues element of G equivalence classes field finite follows fundamental roots fundamental system Hence homomorphism hyperplane induction integer isometry isomorphic K-character of Q LEMMA linear combination linearly independent matrices morphism multiplication N)-pair non-zero obtain operates orthogonal groups p-orbits parabolic subgroups permutation polynomial positive roots PROOF PROPOSITION prove r-chain relations root system root vectors satisfying simple groups simple Lie algebra structure constants subgroup of G subset subspace Suppose symmetric symplectic group system of type THEOREM transforms twisted groups type A1 type G2 Weyl group xr(t xs(u ΓΕΩ λι