Involutions, classical groups, and buildings

JOURNAL OF ALGEBRA

卷:242

Article

Kim, JL ; Moy, A

关键词: nonarchimedean local field;    classical group;    Bruhat-Tits building;    spherical building;    involution;   

DOI  :  10.1006/jabr.2001.8839

来源: Elsevier

【 摘 要 】

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 Aut(k)(G), and we also prove an analogue in the context of affine buildings. (C) 2001 Academic Press.

【 授权许可】

Free