Related papers: Equivariant D-modules on binary cubic forms

We consider groups G which have a cocompact, 3-manifold model for the classifying space \underline{E}G. We provide an algorithm for computing the rationalized equivariant K-homology of \underline{E}G. Under the additional hypothesis that…

We introduce the notion of (twisted) quiver representations in abelian categories and study the category of such representations. We construct standard resolutions and coresolutions of quiver representations and study basic homological…

Laumon moduli spaces are certain smooth closures of the moduli spaces of maps from the projective line to the flag variety of GL_n. We calculate the equivariant cohomology rings of the Laumon moduli spaces in terms of Gelfand-Tsetlin…

To a finite quadratic module, that is, a finite abelian group D together with a non-singular quadratic form Q:D --> Q/Z, it is possible to associate a representation of either the modular group, SL(2,Z), or its metaplectic cover, Mp(2,Z),…

Let $G=G_1 \times G_2$ be a finite group. We know that the second cohomology group $H^2(G,\mathbb C^\times)$ is isomorphic to $H^2(G_1,\mathbb C^\times) \times H^2(G_2,\mathbb C^\times) \times Hom(G_1/G_1' \otimes_\mathbb Z G_2/G_2',…

We construct twisted $\mathcal{D}$-modules on the projective line $\mathbb{P}^1$ that are equivariant for the action of the diagonal torus subgroup of $SL_2$. In the most interesting case these arise as extensions from local systems on…

In this paper we study the problem of explicitly describing the space of invariant linear forms on induced distinguished representations in terms of invariant linear forms on the inducing representation. More precisely, for certain tempered…

We study the category of $\mathbf{P}$-equivariant modules over the infinite variable polynomial ring, where $\mathbf{P}$ denotes the subgroup of the infinite general linear group $\mathbf{GL}(\mathbf{C}^\infty)$ consisting of elements…

An introduction to moduli spaces of representations of quivers is given, and results on their global geometric properties are surveyed. In particular, the geometric approach to the problem of classification of quiver representations is…

A bi-invariant differential 2-form on a Lie group G is a highly constrained object, being determined by purely linear data: an Ad-invariant alternating bilinear form on the Lie algebra of G. On a compact connected Lie group these have an…

Let $G$ and $\check{G}$ be Langlands dual connected reductive groups. We establish a monoidal equivalence of $\infty$-categories between equivariant quasicoherent sheaves on the formal neighborhood of the nilpotent cone in $G$ and…

Let $X$ be a set of $4$ generic points in $\mathbb{P}^2$ with homogeneous coordinate ring $R$. We classify indecomposable graded MCM modules over $R$ by reducing the classification to the Four Subspace problem solved by Nazarova and…

Entanglement transformation of composite quantum systems is investigated in the context of group representation theory. Representation of the direct product group $SL(2,C)\otimes SL(2,C)$, composed of local operators acting on the binary…

We provide an equivariant extension of Carlsson's BGG correspondence in characteristic two. As an application we classify perfect cochain complexes of $(\mathbb{Z}/2\times \mathbb{Z}/2)\rtimes Q$-representations with four-dimensional total…

Let $\mathcal{X} \subset \mathbb{P}_k^d$ be Drinfeld's halfspace over a finite field $k$ and let $\mathcal{E}$ be a homogeneous vector bundle on $\mathbb{P}_k^d$. The paper deals with two different descriptions of the space of global…

We consider representations of quivers taking values in monads or comonads over a Grothendieck category $\mathcal C$. We treat these as scheme like objects whose ``structure sheaf'' consists of monads or comonads. By using systems of…

Let X be a locally symmetric space associated to a reductive algebraic group G defined over Q. L-modules are a combinatorial analogue of constructible sheaves on the reductive Borel-Serre compactification of X; they were introduced in…

We formalize, at the level of D-modules, the notion that A-hypergeometric systems are equivariant versions of the classical hypergeometric equations. For this purpose, we construct a functor on a suitable category of torus equivariant…

Let G be a unipotent algebraic group over an algebraically closed field k of characteristic p > 0 and let l be a prime different from p. Let e be a minimal idempotent in D_G(G), the braided monoidal category of G-equivariant (under…

We make the classical Dickenstein-Sessa canonical representation in local moderate cohomology explicit by an integral formula. We also provide a similar representation of the higher local moderate cohomology groups. The results are related…