Related papers: Tambara-Yamagami, loop groups, bundles and KK-theo…
We study deformations of Fourier-Mukai transforms in general complex analytic settings. We start with two complex manifolds X and Y together with a coherent Fourier-Mukai kernel P on their product. Suppose that P implements an equivalence…
We give a unifying description of all inequivalent vector bundles over the 2-dimensional sphere $S^2$ by constructing suitable global projectors $p$ via equivariant maps. Each projector determines the projective module of finite type of…
The modular transformations of the $(1|1)$ complex supermanifolds in the like-Schottky modular parameterization are discussed. It is shown that these "supermodular" transformations depend on the spinor structure of the supermanifold by…
This is the first of a series of two articles where we construct a version of wrapped Fukaya category $\mathcal W\mathcal F(M\setminus K;H_{g_0})$ of the cotangent bundle $T^*(M \setminus K)$ of the knot complement $M \setminus K$ of a…
In this paper we study the derived categories of coherent sheaves on Grassmannians $\operatorname{Gr}(k,n),$ defined over the ring of integers. We prove that the category $D^b(\operatorname{Gr}(k,n))$ has a semi-orthogonal decomposition,…
We investigate various topological spaces and varieties which can be associated to a block of a finite group scheme G. These spaces come from the theory of cohomological support varieties for modules, as well as from the…
This is a largely expository article based on our previous work on arithmetic diagonal cycles on unitary Shimura varieties. We define a class of Shimura varieties closely related to unitary groups which represent a moduli problem of abelian…
The purpose of this paper is to study categorifications of tensor products of finite dimensional modules for the quantum group for sl(2). The main categorification is obtained using certain Harish-Chandra bimodules for the complex Lie…
In this paper we characterize the fiber representations of equivariant complex vector bundles over a circle and classify these bundles. We also treat the triviality of equivariant complex vector bundles over a circle by investigating the…
We study the representation theory of the rational Cherednik algebra $H_\kappa = H_\kappa({\mathbb Z}_l)$ for the cyclic group ${\mathbb Z}_l = {\mathbb Z} / l {\mathbb Z}$ and its connection with the geometry of the quiver variety…
A near-group fusion category is a fusion category C where all but 1 simple objects are invertible. Examples of these include the Tambara-Yamagami categories and the even sectors of the E6 and affine-D5 subfactors, though there are…
These notes contain an introduction to the theory of complex semisimple quantum groups. Our main aim is to discuss the classification of irreducible Harish-Chandra modules for these quantum groups, following Joseph and Letzter. Along the…
In this paper we prove a family of results connecting the problem of computing cup products in surface bundles to various other objects that appear in the theory of the cohomology of the mapping class group $\operatorname{Mod}_g$ and the…
In this paper we study how to distinguish two embeddings of a finite collection of disjoint circles into the plane up to planar isotopy. We adopt the spirit of the approach by V. Turaev, Operator Invariants of Tangles, Math. USSR-Izv. 35…
We show how quiver representations and their invariant theory natu- rally arise in the study of some moduli spaces parametrizing bundles dened on an algebraic curve, and how they lead to ne results regarding the geometry of these spaces.
We investigate the problem of defining group or loop structures on spheres, where by ''sphere'' we mean the level set q(x) = c of a general K-valued quadratic form q, for an invertible scalar c. When K is a field and q non-degenerate, then…
We study invariants for shifts of finite type obtained as the K-theory of various C*-algebras associated with them. These invariants have been studied intensely over the past thirty years since their introduction by Wolfgang Krieger. They…
We study the relationship between derived categories of factorizations on gauged Landau-Ginzburg models related by variations of the linearization in Geometric Invariant Theory. Under assumptions on the variation, we show the derived…
Differential calculi are obtained for quantum homogeneous spaces by extending Woronowicz' approach to the present context. Representation theoretical properties of the differential calculi are investigated. Connections on quantum…
We establish an isomorphism of complex $K$-theory of the moduli space $\check{\mathcal{M}}$ of $``SL_n"$-Higgs bundles of degree $d$ and rank $n$ (in the sense of Hausel--Thaddeus) and twisted complex $K$-theory of the orbifold…