4 papers
Flat subsets of Euclidean buildings
Raphael Appenzeller, Auguste Hébert, Alexander Lytchak
We prove that any convex flat subset in a complete Euclidean building is contained in an apartment of the maximal system of apartments.
Completed Iwahori-Hecke algebra for Kac-Moody groups over local fields
Auguste Hébert, Dinakar Muthiah
Let be a split Kac-Moody group over a non-Archimedean local field, and let be the Iwahori-Hecke algebra of . In this paper, we construct a completed Iwahori-He…
Tessellations of an affine apartment by affine weight polytopes
Claudio Bravo, Auguste Hébert, Diego Izquierdo +1
Let $\A$ be a finite dimensional vector space and be a finite root system in $\A$. To this data is associated an affine poly-simplicial complex. Motivated by a forthcoming con…
On affine Kazhdan-Lusztig R-polynomials for Kac-Moody groups
Auguste Hébert, Paul Philippe
In 2019, D. Muthiah proposed a strategy to define affine Kazhdan-Lusztig -polynomials for Kac-Moody groups. Since then, Bardy-Panse, the first author and Rousseau have introduce…