Representation Theory and Algebraic Geometry: A Conference Celebrating the Birthdays of Sasha Beilinson and Victor Ginzburg

Description

The chapters in this volume explore the influence of the Russian school on the development of algebraic geometry and representation theory, particularly the pioneering work of two of its illustrious members, Alexander Beilinson and Victor Ginzburg, in celebration of their 60th birthdays. Based on the work of speakers and invited participants at the conference “Interactions Between Representation Theory and Algebraic Geometry”, held at the University of Chicago, August 21-25, 2017, this volume illustrates the impact of their research and how it has shaped the development of various branches of mathematics through the use of D-modules, the affine Grassmannian, symplectic algebraic geometry, and other topics. All authors have been deeply influenced by their ideas and present here cutting-edge developments on modern topics. Chapters are organized around three distinct themes: Groups, algebras, categories, and representation theoryD-modules and perverse sheavesAnalogous varieties defined by quivers Representation Theory and Algebraic Geometry will be an ideal resource for researchers who work in the area, particularly those interested in exploring the impact of the Russian school. Preface Contents Part I Groups, Algebras, Categories, and Their Representation Theory On Semisimplification of Tensor Categories Contents 1 Introduction 2 Preliminaries 2.1 Tensor Ideals 2.2 Semisimplification of a Spherical Tensor Category 2.3 Generalization to Pivotal Karoubian Categories 3 General Results on Semisimplification of Tensor Categories 3.1 Splitting of the Semisimplification Functor for Tannakian Categories in Characteristic Zero, Reductive Envelopes, and the Jacobson-Morozov Lemma 3.2 Compatibility of Semisimplification with Equivariantization 3.3 Compatibility of Negligible Morphisms with Surjective Tensor Functors 4 Semisimplification of Representation Categories of Finite Groups in Characteristic p 4.1 The Result 4.2 Proof of Theorem 4.2 4.3 The Case of Sylow Subgroup*24pt of Prime Order 4.4 The Case of the Symmetric Group Sp+n, where n