相关论文: Representations of elementary abelian p-groups and…

In this talk we discuss the relations between representations of algebraic groups and principal bundles on algebraic varieties, especially in characteristic $p$. We quickly review the notions of stable and semistable vector bundles and…

We introduce and investigate a functorial construction which associates coherent sheaves to finite dimensional (restricted) representations of a restricted Lie algebra $\mathfrak g$. These are sheaves on locally closed subvarieties of the…

Inspired by recent work of Carlson, Friedlander and Pevtsova concerning modules for $p$-elementary abelian groups $E_r$ of rank $r$ over a field of characteristic $p > 0$, we introduce the notions of modules with constant $d$-radical rank…

J. Pevtsova and the author constructed a ``universal $p$-nilpotent operator" for an infinitesimal group scheme $G$ over a field $k$ of characteristic $p > 0$ which led to coherent sheaves on the scheme of 1-parameter subgroups of $G$…

We initiate the investigation of the projective variety $E(r,g)$ of elementary subalgebras of dimension $r$ of a ($p$-restricted) Lie algebra $g$ for some $r > 0$ and demonstrate that this variety encodes considerable information about the…

We describe a new approach for classifying conjugacy classes of elementary abelian subgroups in simple algebraic groups over an algebraically closed field, and understanding the normaliser and centraliser structure of these. For toral…

In this paper, we approach the study of modules of constant Jordan type and equal images modules over elementary abelian p-groups E_r of rank r \geq 2 by exploiting a functor from the module category of a generalized Beilinson algebra…

Algebra bundles, in the strict sense, appear in many areas of geometry and physics. However, the structure of an algebra is flexible enough to vary non-trivially over a connected base, giving rise to a structure of a weak algebra bundle. We…

Let $\mathbb{F}_p$ be the prime field of order $p>0$ and $G$ be an elementary abelian $p$-group.For some $n$-dimensional cohyperplane $G$-representations $V$ over $\mathbb{F}_p$, we show that $\mathbb{F}_p[V\oplus V^*]^G$, the invariant…

Let $\mathbb{k}$ be an algebraically closed field. Connections between representations of the generalized Kronecker quivers $K_r$ and vector bundles on $\mathbb{P}^{r-1}$ have been known for quite some time. This article is concerned with a…

Let $kE$ denote the group algebra of an elementary abelian $p$-group of rank $r$ over an algebraically closed field of characteristic $p$. We investigate the functors $\mathcal{F}_i$ from $kE$-modules of constant Jordan type to vector…

The Weil representation of the symplectic group associated to a finite abelian group of odd order is shown to have a multiplicity-free decomposition. When the abelian group is p-primary, the irreducible representations occurring in the Weil…

Let G be an infinitesimal group scheme over a field k of positive characteristic p. We introduce the global p-nilpotent operator $\Theta_G: k[G] \to k[V(G)]$, where V(G) is the scheme which represents 1-parameter subgroups of G. This…

Let $(\mathfrak{g},[p])$ be a restricted Lie algebra over an algebraically closed field $k$ of characteristic $p\!\ge \!3$. Motivated by the behavior of geometric invariants of the so-called $(\mathfrak{g},[p])$-modules of constant $j$-rank…

We give a new method to construct linear spaces of matrices of constant rank, based on truncated graded cohomology modules of certain vector bundles as well as on the existence of graded Artinian modules with pure resolutions. Our method…

Let G be a connected reductive group defined over an algebraically closed field k of characteristic p > 0. The purpose of this paper is two-fold. First, when p is a good prime, we give a new proof of the ``order formula'' of D. Testerman…

We show how to functorially attach continuous $p$-adic representations of the profinite fundamental group to vector bundles with numerically flat reduction on a proper rigid analytic variety over $\mathbb{C}_p$. This generalizes results by…

Let E be an elementary abelian p-group of rank r and let k be a field of characteristic p. We introduce functors F_i from finitely generated kE-modules of constant Jordan type to vector bundles over projective space of dimension r-1. The…

In this paper we express certain multiplicities in modular representation-theoretic categories of type A in terms of affine p-Kazhdan-Lusztig polynomials. The representation-theoretic categories we deal with include the categories of…

A representation $V$ of an algebraic group $G$ induces a vector bundle $[V/G] \to BG$. The representation $V$ of $G$ is neutral if, for every twisted form $\mathcal{V} \to \mathcal{G}$ of $[V/G] \to BG$ over a field $k$, we have…