Related papers: Localization of modules over small quantum groups

This article is a sequel to hep-th/9411050, q-alg/9412017, q-alg/9503013. Given a collection of $m$ finite factorizable sheaves $\{\CX_k\}$, we construct here some perverse sheaves over configuration spaces of points on a projective line…

The paper is concerned with cohomology of the small quantum group at a root of unity, and of its upper triangular subalgebra, with coefficients in a tilting module. We relate it to a certain t-structure on the derived category of…

The aim of this paper is to provide an overview of the results about classification of quantum groups that were obtained in arXiv:1303.4046 [math.QA] and arXiv:1502.00403 [math.QA].

In this paper we prove the abelian localization theorem for modules over cyclotomic Rational Cherednik algebras.

Clarified certain points and related it to other work.

The aim of the paper is to start to develop the most general theory of localizations/inversion. Several new concepts are introduced and studied.

We present a biequivariant version of Kremnizer-Tanisaki localization theorem for quantum D-modules. We also obtain an equivalence between a category of finitely generated equivariant modules over a quantum group and a category of finitely…

The Hom closed colocalising subcategories of the stable module category of a finite group scheme are classified. This complements the classification of the tensor closed localising subcategories in our previous work. Both classifications…

This paper is a sequel to "Localization of $\frak{u}$-modules. I", hep-th/9411050. We are starting here the geometric study of the tensor category $\cal{C}$ associated with a quantum group (corresponding to a Cartan matrix of finite type)…

This is the foreword to the special volume on localization techniques in quantum field theory. We summarize the individual chapters and their relation.

This is a review article based on a mini-course comprised of four talks given by the author at Berkeley.

In this note we extend the main results of [E. Enochs and S. Estrada, Relative homological algebra in the category of quasi-coherent sheaves. Adv. in Math. 194(2005), 284-295] to the category of cartesian modules over a flat presheaf of…

We consider network models for localisation problems belonging to symmetry class C. This symmetry class arises in a description of the dynamics of quasiparticles for disordered spin-singlet superconductors which have a Bogoliubov - de…

The work is my Ph D thesis (dissertation for obtaining candidate of sciences degree in Russia) fulfilled under direction of D. A. Raikov and defended under supervision of N. Ya. Vilenkin and S. V. Ptchelintsev. In the dissertatin I gave…

This thesis collects my own and collaborative work I have been involved with finding localised systems in quantum field theory that are useful for quantum information. It draws from many well established physical theories such as quantum…

The following paper is devoted to the study of type I locally compact quantum groups. We show how various operators related to the modular theory of the Haar integrals on $\mathbb{G}$ and $\widehat{\mathbb{G}}$ act on the level of direct…

We define and study square-integrable coactions of locally compact quantum groups on Hilbert modules, generalising previous work for group actions. As special cases, we consider square-integrable Hilbert space corepresentations and…

We propose new measures of localization and cooperativity for the analysis of atomic rearrangements. We show that for both clusters and bulk material cooperative rearrangements usually have significantly lower barriers than uncooperative…

Recent ideas on modular localization in local quantum physics are used to clarify the relation between on- and off-shell quantities in particle physics; in particular the relation between on-shell crossing symmetry and off-shell Einstein…

It is well known that the internal suplattices in the topos of sheaves on a locale are precisely the modules on that locale. Using enriched category theory and a lemma on KZ doctrines we prove (the generalization of) this fact in the case…