28 citations · 58 across the 10 of their papers we have counts for
13 papers
A classification of generalized root systems
Michael Cuntz, Bernhard Mühlherr
Dimitrov and Fioresi introduced an object that they call a generalized root system. This is a finite set of vectors in a euclidean space satisfying certain compatibilities between…
Isometries of wall-connected twin buildings
Sebastian Bischof, Bernhard Mühlherr
We introduce the notion of a wall-connected twin building and show that the local-to-global principle holds for these twin buildings. As each twin building satisfying Condition (co…
On isometries of twin buildings
Sebastian Bischof, Anton Chosson, Bernhard Mühlherr
A twin building consists of two buildings that are twinned by a codistance function. We prove that the local structure of a twin building uniquely determines the two buildings up t…
First-Order Aspects of Coxeter Groups
Bernhard Muhlherr, Gianluca Paolini, Saharon Shelah
We lay the foundations of the first-order model theory of Coxeter groups. Firstly, with the exception of the -spherical non-affine case (which we leave open), we characterize th…
On the Tits cone of a Weyl groupoid
Michael Cuntz, Bernhard Mühlherr, Christian J. Weigel
We translate the axioms of a Weyl groupoid with (not necessarily finite) root system in terms of arrangements. The result is a correspondence between Weyl groupoids permitting a ro…
The cone topology on masures
Corina Ciobotaru, Bernhard Mühlherr, Guy Rousseau +1
Masures are generalizations of Bruhat--Tits buildings and the main examples are associated with almost split Kac--Moody groups G over non-Archimedean local fields. In this case, G…
Intrinsic reflections in Coxeter systems
Bernhard Mühlherr, Koji Nuida
Let be a Coxeter system and let . We call a right-angled generator of if or has infinite order for each . We call an intrin…
Quotients of trees for arithmetic subgroups of PGL2 over a rational function field
Ralf Köhl, Bernhard Mühlherr, Koen Struyve
In this note we compute the fundamental domain of the action on the corresponding Bruhat-Tits tree of the arithmetic subgroup of PGL2 with respect to an arbitrary place of the rati…
Descent of affine buildings - I. Large minimal angles
Bernhard Mühlherr, Koen Struyve, Hendrik Van Maldeghem
In this two-part paper we prove an existence result for affine buildings arising from exceptional algebraic reductive groups. Combined with earlier results on classical groups, thi…
Abstract involutions of algebraic groups and of Kac-Moody groups
Ralf Köhl, Max Horn, Bernhard Muhlherr
Based on the second author's thesis in this article we provide a uniform treatment of abstract involutions of algebraic groups and of Kac-Moody groups using twin buildings, RGD sys…
Codistances of 3-spherical buildings
Alice Devillers, Bernhard Mühlherr, Hendrik Van Maldeghem
We show that a 3-spherical building in which each rank 2 residue is connected far away from a chamber, and each rank 3 residue is simply 2-connected far away from a chamber, admits…
The sphericity of the complex of non-degenerate subspaces
Alice Devillers, Ralf Köhl, Bernhard Muhlherr
We prove that the complex of proper non-trivial non-degenerate subspaces of a finite-dimensional vector space endowed with a non-degenerate sesquilinear form is homotopy equivalent…
Isomorphisms of Kac-Moody groups which preserve bounded subgroups
P. -E. Caprace, B. Muehlherr
A subgroup of a Kac-Moody group is called bounded if it is contained in the intersection of two finite type parabolic subgroups of opposite signs. In this paper, we study the isomo…