A Compactification of the Bruhat-Tits Building by Erasmus Landvogt

By Erasmus Landvogt

The objective of this paintings is the definition of the polyhedral compactification of the Bruhat-Tits development of a reductive workforce over a neighborhood box. additionally, an specific description of the boundary is given. with the intention to make this paintings as self-contained as attainable and in addition obtainable to non-experts in Bruhat-Tits conception, the development of the Bruhat-Tits development itself is given completely.

Show description

Read or Download A Compactification of the Bruhat-Tits Building PDF

Similar linear books

LAPACK95 users' guide

LAPACK95 is a Fortran ninety five interface to the Fortran seventy seven LAPACK library. it really is appropriate for a person who writes within the Fortran ninety five language and wishes trustworthy software program for simple numerical linear algebra. It improves upon the unique user-interface to the LAPACK package deal, benefiting from the huge simplifications that Fortran ninety five permits.

Semi-Simple Lie Algebras and Their Representations (Dover Books on Mathematics)

Designed to acquaint scholars of particle physics already accustomed to SU(2) and SU(3) with ideas appropriate to all easy Lie algebras, this article is principally fitted to the learn of grand unification theories. matters contain basic roots and the Cartan matrix, the classical and unheard of Lie algebras, the Weyl crew, and extra.

Lectures on Tensor Categories and Modular Functors

This booklet provides an exposition of the kin one of the following 3 themes: monoidal tensor different types (such as a class of representations of a quantum group), third-dimensional topological quantum box thought, and 2-dimensional modular functors (which evidently come up in 2-dimensional conformal box theory).

Extra info for A Compactification of the Bruhat-Tits Building

Example text

16). Let K/K be the (Galois) splitting field of T and let E = G a l ( / ~ / g ) be the Galois group. Next let r = r S, K) and ~ = O(G, T , / ~ ) be the root systems of G with respect to S and T, respectively, let /~ be a basis of ~ and let /k be a basis of 4~ consisting of restrictions of roots in /~ to S. 16). So we may assume without loss of generality that ~ is ~-invariant. 8 each fibre of the restriction map a ~-+ c~s is a single Galois orbit in/~. We will denote the roots in ~ by small Greek letters and the roots in r by small Latin letters.

Let C E ~ be a chamber. 4) and the topology induced by V ~ coincide, (ii) V C is an open subset of V ~, (iii) the closures of C in V C and V ~ coincide and (iv) the closure of C in V ~ is compact. P r o o f . In order to prove (i) and (ii), it suffices to show that the canonical inclusion V c --+ V ~ is an open embedding. Let C1,C2 E ~ be two chambers, let F C }2 be a face of CI and let U C_ V be 26 an open subset. T h e n c~ n v c~ = c F - n v c~ U+F = (U c vF' +~)n vC~ = F' EE lJ C vF'_ +F F' E~ F'C~ F'C~ F' C C 2 E I where Cu+-f is an open subset of V C1 and V C2 for F ' C F M C1 N C2- Hence Cff N V C2 is an open subset of V C2.

7). S), we obtain w E vWF 1 (--stabilizer of F1 in vW). So by definition we obtain re(x, t) E F1 for all t E]0, 1] and therefore w- re(x, t) = re(x, t), showing the contractibility of V ~. Let F be a face of C. Then the topology on V/(F) induced by V c is the canonical one. Moreover, V is dense in V C. So by definition of the topology on V ~ the assertion (iii) follows. Ad (iv): Let C E ~ be a chamber. 4). Hence the assertion follows. 4) and let 9 = ~(G, S,K) C V* be the root system of the reductive group G.

Download PDF sample

Rated 4.37 of 5 – based on 19 votes

Categories: Linear