Related papers: On homomorphisms involving a hook Weyl module

Let $K$ be an infinite field of characteristic $p>0$ and let $\lambda, \mu$ be partitions, where $\mu$ has two parts. We find sufficient arithmetic conditions on $p, \lambda, \mu$ for the existence of a nonzero homomorphism $\Delta(\lambda)…

Consider the general linear group $G=GL_{n}(K)$ defined over an infinite field $K$ of positive characteristic $p$. We denote by $\Delta(\lambda)$ the Weyl module of $G$ which corresponds to a partition $\lambda$. Let $\lambda, \mu $ be…

We classify all homomorphisms between Weyl modules for SL_3(k) when k is an algebraically closed field of characteristic at least three, and show that the Hom-spaces are all at most one-dimensional. As a corollary we obtain all…

Let $G=GL_n(K)$ be the general linear group defined over an infinite field $K$ of positive characteristic $p$ and let $\Delta(\lambda)$ be the Weyl module of $G$ which corresponds to a partition $\lambda$. In this paper we classify all…

We construct a family of homomorphisms between Weyl modules for affine Lie algebras in characteristic p, which supports our conjecture on the strong linkage principle in this context. We also exhibit a large class of reducible Weyl modules…

Global Weyl modules for generalized loop algebras $\lie g\tensor A$, where $\lie g$ is a simple finite dimensional Lie algebra and A is a commutative associative algebra were defined, for any dominant integral weight $\lambda$, by…

We give a family of pairs of Weyl modules for which the corresponding homomorphism space is at least 2-dimensional. Using this result we show that for fixed parameters $e>0$ and $p\geq 0$ there exist arbitrarily large homomorphism spaces…

We determine the integral extension groups $Ext^1({\Delta}(h),{\Delta}(h(k)))$ and $Ext^k({\Delta}(h),{\Delta}(h(k)))$, where ${\Delta}(h),{\Delta}(h(k))$ are the Weyl modules of the general linear group $GL_n$ corresponding to the hook…

Let K be a subfield of the complex numbers, and let D be the Weyl algebra of K-linear differential operators on K[x_1,...,x_n]. If M and N are holonomic left D-modules we present an algorithm that computes explicit generators for the finite…

We study homogenous Weyl connections with non-positive sectional curvatures. The Cartesian product $\mathbb S^1 \times M$ carries canonical families of Weyl connections with such a property, for any Riemmanian manifold $M$. We prove that if…

Let G be a connected reductive group. To any irreducible G-variety one associates a certain linear group generated by reflections called the Weyl group. Weyl groups play an important role in the study of embeddings of homogeneous spaces. We…

We use the presentation of the Specht modules given by Kleshchev-Mathas-Ram to derive results about Specht modules. In particular, we determine all homomorphisms from an arbitrary Specht module to a fixed Specht module corresponding to any…

The aim of this paper is two fold: First to study finite groups $G$ of automorphisms of the homogenized Weyl algebra $B_{n}$, the skew group algebra $B_{n}\ast G$, the ring of invariants $B_{n}^{G}$, and the relations of these algebras with…

This paper concerns representations of the integral general linear group. The extension groups $Ext^2$ between any pair of hook Weyl modules are determined via a detailed study of cyclic generators and relations associated to certain…

For an arbitrary infinite field k of characteristic p > 0, we describe the structure of a block of the algebraic monoid M_n(k) (all n x n matrices over k), or, equivalently, a block of the Schur algebra S(n,p), whose simple modules are…

Let G be a reductive group over an algebraically closed field whose characteristic is not a bad prime for G. Let w be an elliptic element of the Weyl group which has minimal length in its conjugacy class. We show that there exists a unique…

We define global and local Weyl modules for Lie superalgebras of the form $\mathfrak{g} \otimes A$, where $A$ is an associative commutative unital $\mathbb{C}$-algebra and $\mathfrak{g}$ is a basic Lie superalgebra or $\mathfrak{sl}(n,n)$,…

Given a grading on a nonassociative algebra by an abelian group, we have two subgroups of automorphisms attached to it: the automorphisms that stabilize each homogeneous component (as a subspace) and the automorphisms that permute the…

In this article we study the vertices of simple modules for the symmetric groups in prime characteristic $p$. In particular, we complete the classification of the vertices of simple $S_n$-modules labelled by hook partitions.

In this paper we study a correspondence between cyclic modules over the first Weyl algebra and planar algebraic curves in positive characteristic. In particular, we show that any such curve has a preimage under a morphism of certain…