Buildings and Kac-Moody Groups

Rémy, Bertrand

doi:10.1007/978-1-4614-0709-6_11

Cited by 3 publications

(1 citation statement)

References 54 publications

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“…Being intimately related to deep representation theoretic problems, they attracted great interest for spherical and affine Coxeter groups [KL79]. In recent decades, other Coxeter groups started to attract interest, driven by the theory of buildings and by Kac-Moody groups acting on them [Rém12]. An operator algebraic perspective on Hecke algebras was created by Dymara who introduced Hecke von Neumann algebras N q (W ) associated with a Coxeter system (W, S) and specific deformation parameters q ∈ R S >0 in order to study cohomology of buildings [Dym06;Dav+07].…”

Section: Introductionmentioning

confidence: 99%

Factorial multiparameter Hecke von Neumann algebras and representations of groups acting on right-angled buildings

Raum¹,

Skalski²

2020

Preprint

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We obtain a complete characterisation of factorial multiparameter Hecke von Neumann algebras associated with right-angled Coxeter groups. Considering their p -convolution algebra analogues, we exhibit an interesting parameter dependence, contrasting phenomena observed earlier for group Banach algebras. Translated to Iwahori-Hecke von Neumann algebras, these results allow us to draw conclusions on spherical representation theory of groups acting on right-angled buildings, which are in strong contrast to behaviour of spherical representations in the affine case. We also investigate certain graph product representations of right-angled Coxeter groups and note that our von Neumann algebraic structure results show that these are finite factor representations. Further classifying them up to unitary equivalence allows us to reveal high-dimensional Euclidean subspaces of the space of extremal characters of right-angled Coxeter groups.

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