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Involutions, classical groups and spherical buildings

Authors Kim, Ju Lee
Moy, Allen View this author's profile
Issue Date 2001
Source Journal of Algebra , v. 242, (2), 2001, Aug, p. 495-515
Summary In [Invent. Math.58 (1980), 201-210], Curtis et al. construct a variation of the Tits building. The Curtis-Lehrer-Tits building L(G,k) of a connected reductive k-group G has the important feature that it is a functor from the category of reductive groups defined over a field k and monomorphisms to the category of topological spaces and inclusions. An important consequence derived by Curtis et al. from the functorial nature of the Curtis-Lehrer-Tits building L(G,k) is that if s is a semisimple element of the group G(k) of k-rational points, and G′ is the connected component group of the centralizer of s, then the fixed point set L(G,k)s of s in L(G,k) is the Curtis-Lehrer-Tits building L(G′,k). We generalize this result to arbitrary involutions of Autk(G), and we also prove an analogue in the context of affine buildings. © 2001 Academic Press.
ISSN 00218693
Language English
Format Article
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