Related papers: Large dimensional homomorphism spaces between Weyl…

Roughly speaking, let us say that a map between metric spaces is large scale conformal if it maps packings by large balls to large quasi-balls with limited overlaps. This quasi-isometry invariant notion makes sense for finitely generated…

We prove that the algebra of endomorphisms of a Weyl module of critical level is isomorphic to the algebra of functions on the space of monodromy-free opers on the disc with regular singularity and residue determined by the highest weight…

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 $\mathfrak{sl}(n,n)$,…

We prove a $q$-analogue of the Carter-Payne theorem for the two special cases corresponding to moving an arbitrary number of nodes between adjacent rows, or moving one node between an arbitrary number of rows. As a consequence, we show that…

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…

This paper gives a necessary and sufficient condition for the image of the Specht module under the inverse Schur functor to be isomorphic to the dual Weyl module in characteristic 2, and gives an elementary proof that this isomorphism holds…

Let $G$ be a simple algebraic group of type $E_6$ over an algebraically closed field of characteristic $p>0$. We determine the submodule structure of the Weyl modul es with highest weight $r\omega_1$ for $0\leq r\leq p-1$, where $\omega_1$…

A Riemannian manifold is called Weyl homogeneous, if its Weyl tensors at any two points are "the same", up to a positive multiple. A Weyl homogeneous manifold is modeled on a homogeneous space $M_0$, if its Weyl tensor at every point is…

We define complete stable pairs on a smooth projective variety, and construct their moduli space. These moduli spaces have natural morphisms to the moduli of stable pairs and Quot-schemes. As an example, we show that the moduli of complete…

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…

Let $X$ be a smooth projective curve of genus $g\geq 2$ over the complex numbers. A holomorphic pair on $X$ is a couple $(E,\phi)$, where $E$ is a holomorphic bundle over $X$ of rank $n$ and degree $d$, and $\phi\in H^0(E)$ is a holomorphic…

We consider symmetric (under the action of products of finite symmetric groups) real algebraic varieties and semi-algebraic sets, as well as symmetric complex varieties in affine and projective spaces, defined by polynomials of degrees…

The main goal of our paper is to establish a connection between the Weyl modules of the current Lie superalgebras (twisted and untwisted) attached to $\mathfrak{osp}(1,2)$ and the nonsymmetric Macdonald polynomials of types $A_2^{(2)}$ and…

We show that if a complex has free finitely generated reduced homology groups for two consecutive dimensions and trivial homology for all other dimensions, then it must have the homotopy type of a wedge of spheres of two consecutive…

In this article, we classify the homomorphisms between scalar generalized Verma modules of ${\mathfrak gl}(n, {\mathbb C})$. In fact such homomorphisms are compositions of elementary homomorphisms.

This is partly a survey and partly a research article. Some known results and open problems about Kaehler groups (fundamental groups of compact Kaehler manifolds) are discussed. A new notion of Kaehler homomorphism is introduced. This is a…

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…

Let n be a positive integer and let p be a prime. Suppose that we take a partition of n, and obtain another partition by moving a node from one row to a shorther row. Carter and Payne showed that if the p-residue of the removed and added…

For two discrete metric spaces, $X$ and $Y$ we consider metrics on $X\sqcup Y$ compatible with the metrics on $X$ and $Y$. As morphisms from $X$ to $Y$ we consider the Roe bimodules, i.e. the norm closures of bounded finite propagation…

We study Le Potier's strange duality conjecture on $\mathbb{P}^2$. We show the conjecture is true for the pair ($W(2,0,2),~M(d,0)$) with $d>0$, where $W(2,0,2)$ is the moduli space of semistable sheaves of rank 2, zero first Chern class and…