ﻻ يوجد ملخص باللغة العربية
We study some aspects of modular generalized Springer theory for a complex reductive group $G$ with coefficients in a field $mathbb k$ under the assumption that the characteristic $ell$ of $mathbb k$ is rather good for $G$, i.e., $ell$ is good and does not divide the order of the component group of the centre of $G$. We prove a comparison theorem relating the characteristic-$ell$ generalized Springer correspondence to the characteristic-$0$ version. We also consider Mautners characteristic-$ell$ `cleanness conjecture; we prove it in some cases; and we deduce several consequences, including a classification of supercuspidal sheaves and an orthogonal decomposition of the equivariant derived category of the nilpotent cone.
In this article we formulate and prove the main theorems of the theory of character sheaves on unipotent groups over an algebraically closed field of characteristic p>0. In particular, we show that every admissible pair for such a group G gives rise
In type A we find equivalences of geometries arising in three settings: Nakajimas (``framed) quiver varieties, conjugacy classes of matrices and loop Grassmannians. These are now all given by explicit formulas. As an application we provide a geometri
The nilpotent bicone of a finite dimensional complex reductive Lie algebra g is the subset of elements in g x g whose subspace generated by the components is contained in the nilpotent cone of g. The main result of this note is that the nilpotent bic
Let $G$ be a simply connected algebraic group of type $B,C$ or $D$ over an algebraically closed field of characteristic 2. We construct a Springer correspondence for the dual vector space of the Lie algebra of $G$. In particular, we classify the nilp
Let $G=Sp_{2n}(mathbb{C})$, and $mathfrak{N}$ be Katos exotic nilpotent cone. Following techniques used by Bezrukavnikov in [5] to establish a bijection between $Lambda^+$, the dominant weights for a simple algebraic group $H$, and $textbf{O}$, the s