17 citations · 91 across the 25 of their papers we have counts for
25 papers
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…
Closed sets of real roots in Kac-Moody root systems
Pierre-Emmanuel Caprace, Timothée Marquis
In this note, we provide a complete description of the closed sets of real roots in a Kac-Moody root system.
On the structure of Kac-Moody algebras
Timothée Marquis
Let be a symmetrisable generalised Cartan matrix, and let be the corresponding Kac-Moody algebra. In this paper, we address the following fundamental question…
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…
Half-Lie groups
Timothée Marquis, Karl-Hermann Neeb
In this paper we study the Lie theoretic properties of a class of topological groups which carry a Banach manifold structure but whose multiplication is not smooth. If and …
Positive energy representations of double extensions of Hilbert loop algebras
Timothée Marquis, Karl-Hermann Neeb
A real Lie algebra with a compatible Hilbert space structure (in the sense that the scalar product is invariant) is called a Hilbert-Lie algebra. Such Lie algebras are natural infi…
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…
Isomorphisms of twisted Hilbert loop algebras
Timothée Marquis, Karl-Hermann Neeb
The closest infinite dimensional relatives of compact Lie algebras are Hilbert-Lie algebras, i.e. real Hilbert spaces with a Lie algebra structure for which the scalar product is i…
Positive energy representations for locally finite split Lie algebras
Timothée Marquis, Karl-Hermann Neeb
Let be a locally finite split simple complex Lie algebra of type , , or and be a splitting Cartan subalgebra…
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…