Irreducible Affine Varieties over a Free Group

Affine Deligne-lusztig Varieties in Affine Flag Varieties

This paper studies affine Deligne-Lusztig varieties in the affine flag manifold of a split group. Among other things, it proves emptiness for certain of these varieties, relates some of them to those for Levi subgroups, extends previous conjectures concerning their dimensions, and generalizes the superset method.

Affine Cones over Algebraic Varieties and Embeddings into Toric Prevarieties

Dimensions of Affine Deligne-Lusztig Varieties in Affine Flag Varieties

Affine Deligne-Lusztig varieties are analogs of DeligneLusztig varieties in the context of an affine root system. We prove a conjecture stated in the paper [5] by Haines, Kottwitz, Reuman, and the first named author, about the question which affine DeligneLusztig varieties (for a split group and a basic σ-conjugacy class) in the Iwahori case are non-empty. If the underlying algebraic group is a...

Singularities of Free Group Character Varieties

Let Xr be the moduli of SLn, SUn, GLn, or Un valued representations of a rank r free group. We classify the singular stratification of Xr. This comes down to showing that the singular locus corresponds exactly to reducible representations if there exist singularities at all. Additionally, we show that the moduli Xr are generally not topological manifolds, except for a few examples which we expl...

Irreducible components of characteristic varieties

We give a dimension bound on the irreducible components of the characteristic variety of a system of linear partial di.erential equations de0ned from a suitable 0ltration of the Weyl algebra An. This generalizes an important consequence of the fact that a characteristic variety de0ned from the order 0ltration is involutive. More explicitly, we consider a 0ltration of An induced by any vector (u...