Abstract
Let G be a (connected) reductive algebraic group defined over an algebraically closed field K and let T be a maximal torus of G.LetX be the character group ofTand\(R \subset X\) the root system of Grelative toT.ThusX is isomorphic to \( {\mathbb{Z}^r}\) with r = dim T, the rank of G, and for each \(\alpha \in R\) there exists a unipotent subgroup \({U_\alpha }\) which is isomorphic to the additive group of K and is normalized by T according to the character \(\alpha \):1.1 If \({u_\alpha }:K \to {U_\alpha }\) is an isomorphism then \(t{u_\alpha }\left( a \right){t^{ - 1}} = {u_\alpha }\left( {\alpha \left( t \right)a} \right) \)for all\(t \in T\)and \(a \in K. \)
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© 1998 Springer Science+Business Media Dordrecht
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Steinberg, R. (1998). The Isomorphism and Isogeny Theorems for Reductive Algebraic Groups. In: Carter, R.W., Saxl, J. (eds) Algebraic Groups and their Representations. NATO ASI Series, vol 517. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5308-9_12
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DOI: https://doi.org/10.1007/978-94-011-5308-9_12
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