Related papers: Chimney retractions in affine buildings encode orb…
This paper provides a unified combinatorial framework to study orbits in certain affine flag varieties via the associated Bruhat-Tits buildings. We first formulate, for arbitrary affine buildings, the notion of a chimney retraction. This…
This survey is about combinatorial objects related to reflection groups and their applications in representation theory and arithmetic geometry. Coxeter groups and folded galleries in Coxeter complexes are introduced in detail and…
We characterize folding patterns, the combinatorial options of folding minimal alcove-to-alcove galleries in affine Coxeter complexes positively with respect to Weyl chamber orientations of the Coxeter complex, by drawing a connection to…
We consider affine buildings with refined chamber structure. For each vertex in the refined chamber structure we construct a contraction, based at the vertex, that is used to prove exactness of Schneider-Stuhler resolutions of arbitrary…
Positive configurations of points in the affine building were introduced in \cite{Le} as the basic object needed to define higher laminations. We start by giving a self-contained, elementary definition of positive configurations of points…
We prove an analogue of Kostants convexity theorem for thick affine buildings and give an application for groups with affine BN-pair. Recall that there are two natural retractions of the affine building onto a fixed apartment A: The…
We classify affine varieties with an action of a connected, reductive algebraic group such that the group is isomorphic to an open orbit in the variety. This is accomplished by associating a set of one-parameter subgroups of the group to…
The notion of convexity in tropical geometry is closely related to notions of convexity in the theory of affine buildings. We explore this relationship from a combinatorial and computational perspective. Our results include a convex hull…
Affine buildings are in a certain sense analogs of symmetric spaces. It is therefore natural to try to find analogs of results for symmetric spaces in the theory of buildings. In this paper we prove a version of Kostant's convexity theorem…
Matsuki and Oshima introduced the notion of clans, which are incomplete matchings with positive or negative signs on isolated vertices. They discovered that clans parametrise $K$-orbits in the flag varieties for classical linear groups,…
In this two-part paper we prove an existence result for affine buildings arising from exceptional algebraic reductive groups. Combined with earlier results on classical groups, this gives a complete and positive answer to the conjecture…
In this two-part paper we prove an existence result for affine buildings arising from exceptional algebraic reductive groups. Combined with earlier results on classical groups, this gives a complete and positive answer to the conjecture…
In this paper we will first introduce the notion of affine structures on a ringed space and then obtain several properties. Affine structures on a ringed space, arising mainly from complex analytical spaces of algebraic schemes over number…
We construct the affine version of the Fomin-Kirillov algebra, called the affine FK algebra, to investigate the combinatorics of affine Schubert calculus for type $A$. We introduce Murnaghan-Nakayama elements and Dunkl elements in the…
In this article we work out the details of flat groups of the automorphism group of locally finite Bruhat-Tits buildings.
We discuss the classification of reflection subgroups of finite and affine Weyl groups from the point of view of their root systems. A short case free proof is given of the well known classification of the isomorphism classes of reflection…
I extend the ramified geometric Satake equivalence of Zhu from tamely ramified groups to include the case of general connected reductive groups. As a prerequisite I prove basic results on the geometry of affine flag varieties.
We investigate Bruhat-Tits buildings and their compactifications by means of Berkovich analytic geometry over complete non-Archimedean fields. For every reductive group G over a suitable non-Archimedean field k we define a map from the…
We develop a theory of affine flag varieties and of their Schubert varieties for reductive groups over a Laurent power series local field k((t)) with k a perfect field. This can be viewed as a generalization of the theory of affine flag…
I extend the framework of rigid analytic geometry to the setting of algebraic geometry relative to monoids, and study the associated notions of separated, proper, and overconvergent morphisms. The category of affine manifolds embeds as a…