Involutions, Classical Groups, and Buildings

✍ Scribed by Ju-Lee Kim; Allen Moy

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 173 KB
• Volume: 242
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.2001.8839

✦ Synopsis

In [Invent. Math. 58 (1980), 201-210], Curtis et al. construct a variation of the Tits building. The Curtis-Lehrer-Tits building (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 (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 (G, k s of s in (G, k) is the Curtis-Lehrer-Tits building (G k). We generalize this result to arbitrary involutions of Aut k (G), and we also prove an analogue in the context of affine buildings.