Related papers: Generalized affine Springer fibers

We develop a theory of singular support for various infinite dimensional stacks and establish several functoriality properties. Then we apply this theory to compute the singular support of the Grothendieck-Springer affine Springer sheaf and…

We establish dimension formulas for the Witt vector affine Springer fibers associated to a reductive group over a mixed characteristic local field, under the assumption that the group is essentially tamely ramified and the residue…

We introduce parabolic multiplicative affine Springer fibers, which resemble the admissible union of affine Deligne Lusztig varieties in the affine flag variety. We also study their global counterparts called parabolic multiplicative…

For the group $\mathrm{GL}_{d}$, we confirm a conjecture of Goresky, Kottwitz and MacPherson, which states that the cohomology of the affine Springer fibers depend only on the root valuation datum of their defining elements. The proof…

According to Laumon, an affine Springer fiber is homeomorphic to the universal abelian covering of the compactified Jacobian of a spectral curve. We construct equivariant deformations $f_{n}:\overline{\mathcal{P}}_{n}\to \mathcal{B}_{n}$ of…

We study basic geometric properties of some group analogue of affine Springer fibers and compare with the classical Lie algebra affine Springer fibers. The main purpose is to formulate a conjecture that relates the number of irreducible…

We show that Hilbert schemes of planar curve singularities and their parabolic variants can be interpreted as certain generalized affine Springer fibers for $GL_n$, as defined by Goresky-Kottwitz-MacPherson. Using a generalization of affine…

We identify, up to homeomorphisms, the affine Springer fibers for GL(n) on a local field of equal characteristics with some coverings of compactified jacobians of singular projective curves. This allows us to prove an irreducibility…

We establish several foundational results regarding the Grothendieck-Springer affine fibration. More precisely, we prove some constructibility results on the affine Grothendieck-Springer sheaf and its coinvariants, enrich it with a group of…

We study basic geometric properties of Kottwitz-Viehmann varieties, which are certain generalizations of affine Springer fibers that encode orbital integrals of spherical Hecke functions. Based on previous work of A. Bouthier and the…

We explain an algorithm to calculate Arthur's weighted orbital integral in terms of the number of rational points on the fundamental domain of the associated affine Springer fiber. The strategy is to count the number of rational points of…

Assuming the purity conjecture for the affine Springer fibers which has been formulated by Goresky, Kottwitz and MacPherson, we prove a geometric analog of the fundamental lemma for unitary groups. Our approach is similar to the one of…

An affine Hopf fibration is a fibration of n-dimensional real affine space by p-dimensional pairwise skew affine subspaces. An example is a fibration of 3-space by pairwise skew lines, the result of the central projection of the classical…

We prove the cohomological purity of punctual Hilbert schemes of points on generic irreducible planar curve singularities, by constructing an explicit affine paving. Via their identification with generalized $GL_N$-affine Springer fibers…

We consider a new stratification of the space of configurations of $n$ marked points on the complex plane. Recall that this space can be differently interpreted as the space $^{\rm D}{\rm Pol}_{n}$ of degree $n>1$ complex, monic polynomials…

Following Steinberg, we construct an adjoint quotient for the Vinberg semi-group and a section to this quotient. Then, after Ng\^o, we show the existence of a regular centralizer on it and use it to compute the affine Springer fibers for…

We show that representations of convolution algebras such as Lustzig's graded affine Hecke algebra or the quiver Hecke algebra and quiver Schur algebra in (affine) type A can be realised in terms of certain equivariant motivic sheaves…

We state a conjecture on how to construct affine pavings for cohomologically pure projective algebraic varieties, which admit an action of torus such that the fixed points and $1$-dimensional orbits are finite. Experiments on the affine…

This paper defines and studies a stratification of the adjoint quotient of the Lie algebra of a reductive group over a Laurent power series field. The stratification arises naturally in the context of affine Springer fibers.

For $G$ a connected reductive group, $\gamma\in \kg(F)$ semisimple regular integral, we introduce a fundamental domain $F_{\gamma}$ for the affine Springer fibers $\xx_{\gamma}$. There is a beautiful way to reduce the purity conjecture of…