Complete Reducibility In Euclidean Twin Buildings
In , J.P. Serre defined completely reducible subcomplexes of spherical buildings in order to study subgroups of reductive algebraic groups. This paper begins the exploration of how one may use a similar notion of completely reducible subcomplexes of twin buildings to study subgroups of algebraic groups over a ring of Laurent polynomials and Kac-Moody groups. In this paper we explore the definitions of convexity and complete reducibility in twin buildings and some implications of the two in the Euclidean case.
Buildings; Complete Reducibility; twin buildings
Brown, Kenneth Stephen
Vogtmann, Karen L; Speh, Birgit Else Marie
Ph. D., Mathematics
Doctor of Philosophy
dissertation or thesis