Related papers: Twisted Jacquet modules: a conjecture of D. Prasad

We study the general properties of commutative differential graded algebras in the category of representations over a reductive algebraic group with an injective central cocharacter. Besides describing the derived category of differential…

The central topic is this question: is a given $k$-\'etale algebra $\prod_lE_l/k$ the specialization of a given $k$-cover $f:X\rightarrow B$ at some point $t_0\in B(k)$? Our main tool is a {\it twisting lemma} that reduces the problem to…

In this paper we analyze the structure of some subalgebras of quantized enveloping algebras corresponding to unipotent and solvable subgroups of a simple Lie group G. These algebras have the non--commutative structure of iterated algebras…

In this paper, we prove the categories of lower bounded twisted modules of positive integer levels for simple vertex operator algebras associated with affine Lie algebras and general automorphisms are semisimple, using the twisted…

On a smooth projective variety with k ample line bundles, we denote by Z the complete intersection subvariety defined by generic sections. We define the twisted quantum D-module which is a vector bundle with a flat connection, a flat…

We are continuing our study of ADE-orbifold subalgebras of the triplet vertex algebra W(p). This part deals with the dihedral series. First, subject to a certain constant term identity, we classify all irreducible modules for the vertex…

We propose a notion of algebra of {\it twisted} chiral differential operators over algebraic manifolds with vanishing 1st Pontrjagin class. We show that such algebras possess families of modules depending on infinitely many complex…

The generalized chain geometry over the local ring $K(\epsilon;\sigma)$ of twisted dual numbers, where $K$ is a finite field, is interpreted as a divisible design obtained from an imprimitive group action. Its combinatorial properties as…

We determine the invariants, with arbitrary determinant twists, of the parabolic subgroups of the finite general linear group GL_n(q) acting on the tensor product of the symmetric algebra and the exterior algebra of the natural…

Let F be a non-archimedean local field with residue characteristic p. Let l be a prime number different from p. Let G be a connected reductive group which is split, semi-simple, and simply connected. On the one hand, we describe the…

We study arithmetic intersections on twisted (quaternionic) Hilbert modular surfaces and Shimura curves over a real quadratic field. Our first main result is the determination of the degree of the top arithmetic Todd class of an arithmetic…

We investigate the representation theory of domestic group schemes $\mathcal{G}$ over an algebraically closed field of characteristic $p > 2$. We present results about filtrations of induced modules, actions on support varieties, Clifford…

We use enhanced Langlands parameters to obtain a classification for irreducible representations of twisted $p$-adic general linear groups in unramified principal series. We give the definition of standard representations and prove the…

Let $G$ be connected reductive algebraic group defined over an algebraically closed field of characteristic $p > 0$ and suppose that $p$ is a good prime for the root system of $G$, the derived subgroup of $G$ is simply connected and the Lie…

Let $\theta$ and $\theta'$ be a pair of exceptional representations in the sense of Kazhdan and Patterson [KP], of a metaplectic double cover of $GL_n$. The tensor $\theta\otimes\theta'$ is a (very large) representation of $GL_n$. We…

We show how the modular representation theory of inner forms of general linear groups over a non-Archimedean local field can be brought to bear on the complex theory in a remarkable way. Let F be a non-Archimedean locally compact field of…

The main goal of this paper is to prove the Schmidt--Kolchin conjecture. This conjecture says the following: the vector space of degree \(d\) differentially homogeneous polynomials in \((N+1)\) variables is of dimension \((N+1)^{d}\). Next,…

We propose a global Jacquet-Langlands correspondence for the modules over the von Neumann algebras of $S$-arithmetic subgroups of $\rm{GL}(2)$ and of a quaternion algebra $D$, which are both defined over a totally real number field $F$. If…

Let $G$ be a connected reductive group defined over a non-Archimedean local field $F$ of residue characteristic $p$. Let $\ell$ be a prime number distinct from $p$. Let $E$ be a cyclic Galois extension of $F$ with $[E:F]=\ell$. Let $\Pi$ be…

We begin a study of torsion theories for representations of an important class of associative algebras over a field which includes all finite W-algebras of type A, in particular the universal enveloping algebra of gl(n) (or sl(n)) for all…