17 citations · 91 across the 25 of their papers we have counts for
19 papers · 1 filter
Presentation and uniqueness of Kac-Moody groups over local rings
Timothée Marquis, Bernhard Mühlherr
To any generalised Cartan matrix (GCM) and any ring , Tits associated a Kac-Moody group defined by a presentation à la Steinberg. For a domain with f…
Describing the nub in maximal Kac-Moody groups
Sebastian Bischof, Timothée Marquis
Let be a totally disconnected locally compact (tdlc) group. The contraction group of an element is the set of all such that $g^n h g^{-n} \t…
Stable reflection length in Coxeter groups
Francesco Fournier-Facio, Marco Lotz, Timothée Marquis
We introduce stable reflection length in Coxeter groups, as a way to study the asymptotic behaviour of reflection length. This creates connections to other well-studied stable leng…
Amalgams of rational unipotent groups and residual nilpotence
Pierre-Emmanuel Caprace, Timothée Marquis
We provide sufficient conditions for a free amalgamated product of torsionfree nilpotent groups to be residually nilpotent. We also characterise the residual nilpotence of certain…
Minicourse on Kac-Moody groups
Timothée Marquis
These are informal lecture notes for a three-hour minicourse on Kac-Moody groups, given at the workshop "Kac-Moody geometry" in July 2023 in Kiel. They provide a concise overview o…
On the centre of Iwahori-Hecke algebras
Timothée Marquis, Sven Raum
We prove triviality of the centre of arbitrary Hecke algebras of irreducible non-finite non-affine type. This result is obtained as a consequence of the following structure result…
Locally normal subgroups and ends of locally compact Kac-Moody groups
Pierre-Emmanuel Caprace, Timothée Marquis, Colin D. Reid
A locally normal subgroup in a topological group is a subgroup whose normaliser is open. In this paper, we provide a detailed description of the large-scale structure of closed loc…
Growing trees from compact subgroups
Pierre-Emmanuel Caprace, Timothée Marquis, Colin D. Reid
We establish a new connection between local and large-scale structure in compactly generated totally disconnected locally compact (t.d.l.c.) groups , finding a sufficient condit…
Structure of conjugacy classes in Coxeter groups
Timothée Marquis
This paper gives a definitive solution to the problem of describing conjugacy classes in arbitrary Coxeter groups in terms of cyclic shifts. Let be a Coxeter system. A cycl…
Hyperfiniteness of boundary actions of hyperbolic groups
Timothée Marquis, Marcin Sabok
We prove that for every finitely generated hyperbolic group , the action of on its Gromov boundary induces a hyperfinite equivalence relation.
Cyclically reduced elements in Coxeter groups
Timothée Marquis
Let be a Coxeter group. We provide a precise description of the conjugacy classes in , in the spirit of Matsumoto's theorem. This extends to all Coxeter groups an important…
On geodesic ray bundles in buildings
Timothée Marquis
Let be a building, identified with its Davis realisation. In this paper, we provide for each and each in the visual boundary of a description of t…
Around the Lie correspondence for complete Kac-Moody groups and Gabber-Kac simplicity
Timothée Marquis
Let be a field and be a generalised Cartan matrix, and let be the corresponding minimal Kac-Moody group of simply connected type over . Consider the…
Conjugacy classes and straight elements in Coxeter groups
Timothée Marquis
Let W be a Coxeter group. In this paper, we establish that, up to going to some finite index normal subgroup W_0 of W, any two cyclically reduced expressions of conjugate elements…
Abstract simplicity of locally compact Kac-Moody groups
Timothée Marquis
In this paper, we establish that complete Kac-Moody groups over finite fields are abstractly simple. The proof makes an essential use of Mathieu-Rousseau's construction of complete…
A fixed point theorem for Lie groups acting on buildings and applications to Kac-Moody theory
Timothée Marquis
We establish a fixed point property for a certain class of locally compact groups, including almost connected Lie groups and compact groups of finite abelian width, which act by si…
Open subgroups of locally compact Kac-Moody groups
Pierre-Emmanuel Caprace, Timothée Marquis
Let G be a complete Kac-Moody group over a finite field. It is known that G possesses a BN-pair structure, all of whose parabolic subgroups are open in G. We show that, conversely,…
Can an anisotropic reductive group admit a Tits system?
Pierre-Emmanuel Caprace, Timothée Marquis
Seeking for a converse to a well-known theorem by Borel-Tits, we address the question whether the group of rational points G(k) of an anisotropic reductive k-group may admit a spli…
Angle-deformations in Coxeter groups
Timothée Marquis, Bernhard Mühlherr
The isomorphism problem for Coxeter groups has been reduced to its 'reflection preserving version' by B. Howlett and the second author. Thus, in order to solve it, it suffices to d…