Related papers: Equivariant Vector Bundles with Connection on Drin…

Let $\mathcal{A}$ be a near-group fusion category of type $\mathbb{Z}_3+6$. We show that there is a modular tensor equivalence…

We consider the finite generation property for cohomology of a finite tensor category C, which requires that the self-extension algebra of the unit Ext*_C(1,1) is a finitely generated algebra and that, for each object V in C, the graded…

Let X be an algebraic variety with an action of an algebraic group G. Suppose X has a full exceptional collection of sheaves, and these sheaves are invariant under the action of the group. We construct a semiorthogonal decomposition of…

Let G be a split connected reductive group over a finite field F_q, and N its maximal unipotent subgroup. V. Drinfeld has introduced a remarkable partial compactification of the moduli stack of N-bundles on a smooth projective curve X over…

We define a diffeology on the Milnor classifying space of a diffeological group $G$, constructed in a similar fashion to the topological version using an infinite join. Besides obtaining the expected classification theorem for smooth…

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 develop an equivariant Dixmier-Douady theory for locally trivial bundles of $C^*$-algebras with fibre $D \otimes \mathbb{K}$ equipped with a fibrewise $\mathbb{T}$-action, where $\mathbb{T}$ denotes the circle group and $D =…

We prove that the parallel transport of a flat $n-1$-gerbe on any given target space gives rise to an $n$-dimensional extended homotopy quantum field theory. In case the target space is the classifying space of a finite group, we provide…

Recently, Gekeler proved that the group of invertible analytic functions modulo constant functions on Drinfeld's upper half space is isomorphic to the dual of an integral generalized Steinberg representation. In this note we show that the…

Let $(F,J,\omega)$ be an almost K\"ahler manifold, $\alpha$ a $J$-holomorphic action of a compact Lie group $\hat K$ on $F$, and $K$ a closed normal subgroup of $\hat K$ which leaves $\omega$ invariant. We introduce gauge theoretical…

Equivariant $\Gamma$-spaces model equivariant infinite loop spaces. In this article, we show that there exists a connective Quillen equivalence between the category of equivariant $\Gamma$-spaces and the category of orthogonal spectra.

We compare the invariants of flat vector bundles defined by Atiyah et al. and Jones et al. and prove that, up to weak homotopy, they induce the same map, denoted by $e$, from the $0$-connective algebraic $K$-theory space of the complex…

We prove that the Drinfeld double of an arbitrary finite group scheme has finitely generated cohomology. That is to say, for G any finite group scheme, and D(G) the Drinfeld double of the group ring kG, we show that the self-extension…

We give an answer to the abstract Capelli problem: Let $(G, V)$ be a multiplicity-free finite-dimensional representation of a connected reductive complex Lie group $G$ and $G'$ be its derived subgroup. Assume that the categorical quotient…

This work is motivated by a result of Drinfeld on Poisson homogeneous spaces. For each Poisson manifold $P$ with a Poisson action by a Poisson Lie group $G$, we describe a Lie algebroid structure on the direct sum vector bundle $P \times…

Let F be a smooth real manifold with a linear connection in the tangent bundle. How can we extend the coefficients of the connection to bi-differential operators that incorporate the original structure at zero order? Take a constant mapping…

Let $\mathcal{C}$ be a spherical fusion category. The goal of this article is to present the tube category of $\mathcal{C}$, denoted $\mathcal{TC}$, as giving an alternative graphical perspective on the Drinfeld centre of $\mathcal{C}$,…

A basic question for any property of quasi--coherent sheaves on a scheme $X$ is whether the property is local, that is, it can be defined using any open affine covering of $X$. Locality follows from the descent of the corresponding module…

Let $X$ be a variety with an action by an algebraic group $G$. In this paper we discuss various properties of $G$-equivariant $D$-modules on $X$, such as the decompositions of their global sections as representations of $G$ (when $G$ is…

Let $G$ be a complex reductive group. A folklore result asserts the existence of an $\mathbb{E}_2$-algebra structure on the Ran Grassmannian of $G$ over $\mathbb{A}^1_{\mathbb{C}}$, seen as a topological space with the complex-analytic…