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A note on the Tits systems of Kac-Moody Steinberg groups. (English) Zbl 0910.22019
Let \(G\) and \(H\) denote the Chevalley (adjoint) and the Steinberg (nonadjoint) Kac-Moody group corresponding to a Kac-Moody algebra \(L\), respectively. Let \(\sigma\) denote the canonical homomorphism of \(H\) onto \(G\) which by an earlier result of the author is a canonical group map of the Weyl simple subgroup of \(H\) onto \(G\). In this note the author proves that the \(\sigma\)-inverse image of a Tits system in \(G\) forms a Tits system in the Weyl simple subgroup of \(H\).
MSC:
22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
20E42 Groups with a \(BN\)-pair; buildings
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