On Tits’ Centre Conjecture for Fixed Point Subcomplexes
نویسنده
چکیده
We give a short and uniform proof of a special case of Tits’ Centre Conjecture using a theorem of J-P. Serre [8] and a result from [1]. Precisely, we show that this conjecture holds for fixed point subcomplexes X of the building X = X(G) of a connected reductive algebraic group G, where H is a subgroup of G.
منابع مشابه
On Tits’ Centre Conjecture for Fixed Point Subcomplexes
We give a short and uniform proof of a special case of Tits’ Centre Conjecture using a theorem of J-P. Serre [8] and a result from [1]. We consider fixed point subcomplexes X of the building X = X(G) of a connected reductive algebraic group G, where H is a subgroup of G.
متن کاملThe center conjecture for thick spherical buildings
We prove that a convex subcomplex of a spherical building of type E7 or E8 is a subbuilding or the group of building automorphisms preserving the subcomplex has a fixed point in it. Together with previous results of Mühlherr-Tits, and Leeb and the author, this completes the proof of Tits’ Center Conjecture for thick spherical buildings.
متن کاملNo : 19 Title : ‘ the Strong Centre Conjecture : an Invariant Theory Approach
The aim of this note is to describe an approach to a strong form of J. Tits’ Centre Conjecture for spherical buildings. This is accomplished by generalizing a fundamental result of G.R. Kempf from Geometric Invariant Theory and by interpreting this generalization in the context of spherical buildings. We are able to recapture the conjecture entirely in terms of our generalization of Kempf’s not...
متن کاملEssays on representations of real groups Symmetric spaces of semi-simple groups
In Cartan’s original proof, the fixed point theorem was about Riemannian spaces of negative curvature, but I’ll use instead a simpler geometric notion due to [Bruhat-Tits:1972]. This allows an argument that is somewhat shorter and more direct than the standard one presented, for example, in [Helgason:1968]. The original application of the criterion of Bruhat-Tits was to buildings, as explained ...
متن کاملThe Action of Thompson’s Group on a Cat(0) Boundary
For a given locally finite CAT(0) cubical complex X with base vertex ∗, we define the profile of a given geodesic ray c issuing from ∗ to be the collection of all hyperplanes (in the sense of [17]) crossed by c. We give necessary conditions for a collection of hyperplanes to form the profile of a geodesic ray, and conjecture that these conditions are also sufficient. We show that profiles in di...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009