The Thick Frame of a Weak Twin Building

Abstract

Abstract We prove the following extension to twin buildings of a result for spherical buildings which appears in [11]: to every weak twin building ∆, there is canonically associated a thick twin building ∆̄ whose Weyl group W (∆̄) can be considered as a reflection subgroup of the Weyl group W(∆) of ∆; conversely, it is possible to recover ∆ from the thick twin building ∆̄ and from the inclusion W(∆̄), ↪ W(∆).