Guy Rousseau
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View article: Split Kac-Moody groups over a local field, II. Ordered masures
Split Kac-Moody groups over a local field, II. Ordered masures Open
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 whe…
View article: In memoriam: Jacques E. Dumont (1931-2023)
In memoriam: Jacques E. Dumont (1931-2023) Open
OPINION article Front. Endocrinol., 16 March 2023Sec. Molecular and Structural Endocrinology Volume 14 - 2023 | https://doi.org/10.3389/fendo.2023.1171677
View article: Twin masures associated with Kac-Moody groups over Laurent polynomials
Twin masures associated with Kac-Moody groups over Laurent polynomials Open
Let $\mathfrak{G}$ be a split reductive group, $\mathbb{k}$ be a field and $\varpi$ be an indeterminate. In order to study $\mathfrak{G}(\mathbb{k}[\varpi,\varpi^{-1}])$ and $\mathfrak{G}(\mathbb{k}(\varpi))$, one can make them act on thei…
View article: The cone topology on masures
The cone topology on masures Open
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 strongly transitively on its corresponding masure Δ as w…
View article: On structure constants of Iwahori-Hecke algebras for Kac-Moody groups
On structure constants of Iwahori-Hecke algebras for Kac-Moody groups Open
We consider the Iwahori-Hecke algebra associated to an almost split Kac-Moody group $G$ (affine or not) over a nonarchimedean local field $K$. It has a canonical double-coset basis $(T_{\mathbf w})_{\mathbf w\in W^+}$ indexed by a sub-semi…
View article: Macdonald's formula for Kac–Moody groups over local fields
Macdonald's formula for Kac–Moody groups over local fields Open
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View article: Almost split Kac–Moody groups over ultrametric fields
Almost split Kac–Moody groups over ultrametric fields Open
For a split Kac–Moody group G over an ultrametric field K , S. Gaussent and the author defined an ordered affine hovel (for short, a masure) on which the group acts; it generalizes the Bruhat–Tits building which corresponds to the case whe…
View article: The cone topology on masures
The cone topology on masures Open
This preprint improves the essential results in the preprint ``Strongly transitive actions on affine ordered hovels'' by Corina Ciobotaru and Guy Rousseau.
View article: Strongly transitive actions on affine ordered hovels
Strongly transitive actions on affine ordered hovels Open
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 corresponding hovel $Δ$ as well as on th…