# Groupes de Kac-Moody d\'eploy\'es sur un corps local, II Masures ordonn\'ees

@article{Rousseau2010GroupesDK, title={Groupes de Kac-Moody d\'eploy\'es sur un corps local, II Masures ordonn\'ees}, author={Guy Rousseau}, journal={arXiv: Group Theory}, year={2010} }

For a split Kac-Moody group (in J. Tits' definition) over a field endowed with a real valuation, we build an ordered affine hovel on which the group acts. This construction generalizes the one already done by S. Gaussent and the author when the residue field contains the complex field [Annales Fourier, 58 (2008), 2605-2657] and the one by F. Bruhat and J. Tits when the group is reductive. We prove that this hovel has all properties of ordered affine hovels (masures affines ordonn\'ees) as…

## 29 Citations

Iwahori-Hecke algebras for Kac-Moody groups over local fields

- Mathematics
- 2014

We define the Iwahori-Hecke algebra for an almost split Kac-Moody group over a local non-archimedean field. We use the hovel associated to this situation, which is the analogue of the Bruhat-Tits…

Topological Kac-Moody groups and their subgroups

- Mathematics
- 2013

Kac–Moody groups may be viewed as infinite-dimensional analogues of semi-simple Lie groups, or else semi-simple algebraic groups. More precisely, one first considers Kac–Moody algebras, which are —…

Spherical Hecke algebras for Kac-Moody groups over local fields

- Mathematics
- 2012

We define the spherical Hecke algebra H for an almost split Kac-Moody group G over a local non-archimedean field. We use the hovel I associated to this situation, which is the analogue of the…

Macdonald's formula for Kac–Moody groups over local fields

- MathematicsProceedings of the London Mathematical Society
- 2019

For an almost split Kac–Moody group G over a local non‐Archimedean field, the last two authors constructed a spherical Hecke algebra sH (over C , say) and its Satake isomorphism S with the…

Almost split Kac-Moody groups over ultrametric fields

- Mathematics
- 2012

For a split Kac-Moody group G over an ultrametric field K, S. Gaussent and the author defined an ordered affine hovel on which the group acts; it generalizes the Bruhat-Tits building which…

The cone topology on masures

- Mathematics
- 2017

Abstract 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 acts…

Kac-Moody Lie algebras graded by Kac-Moody root systems

- Mathematics
- 2012

We look to gradations of Kac-Moody Lie algebras by Kac-Moody root systems with finite dimensional weight spaces. We extend, to general Kac-Moody Lie algebras, the notion of C-admissible pair as…

Completed Iwahori-Hecke algebras and parahoric Hecke algebras for Kac-Moody groups over local fields

- MathematicsJournal de l’École polytechnique — Mathématiques
- 2019

Let G be a split Kac-Moody group over a non-archimedean local field. We define a completion of the Iwahori-Hecke algebra of G. We determine its center and prove that it is isomorphic to the spherical…

Strongly transitive actions on affine ordered hovels

- Mathematics
- 2015

A hovel is a generalization of the Bruhat–Tits building that is associated to an almost split Kac–Moody group G over a non-Archimedean local field. In particular, G acts strongly transitively on its…

Kato's irreducibility criterion for Kac-Moody groups over local fields

- Mathematics
- 2021

In 2014, Braverman, Kazhdan, Patnaik and Bardy-Panse, Gaussent and Rousseau associated Iwahori-Hecke algebras to Kac-Moody groups over non-Archimedean local fields. In a previous paper, we defined…