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OverviewSince its inception around 1980, the theory of perverse sheaves has been a vital tool of fundamental importance in geometric representation theory. This book, which aims to make this theory accessible to students and researchers, is divided into two parts. The first six chapters give a comprehensive account of constructible and perverse sheaves on complex algebraic varieties, including such topics as Artin's vanishing theorem, smooth descent, and the nearby cycles functor. This part of the book also has a chapter on the equivariant derived category, and brief surveys of side topics including etale and $\ell$-adic sheaves, $\mathcal{D}$-modules, and algebraic stacks. The last four chapters of the book show how to put this machinery to work in the context of selected topics in geometric representation theory: Kazhdan-Lusztig theory; Springer theory; the geometric Satake equivalence; and canonical bases for quantum groups. Recent developments such as the $p$-canonical basis are also discussed. The book has more than 250 exercises, many of which focus on explicit calculations with concrete examples. It also features a 4-page ``Quick Reference'' that summarizes the most commonly used facts for computations, similar to a table of integrals in a calculus textbook. Full Product DetailsAuthor: Pramod N. AcharPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.882kg ISBN: 9781470455972ISBN 10: 1470455978 Pages: 562 Publication Date: 30 August 2022 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsSheaf theory Constructible sheaves on complex algebraic varieties Perverse sheaves Nearby and vanishing cycles Mixed sheaves Equivariant derived categories Kazhdan-Lusztig theory Springer theory The geometric Satake equivalence Quiver representations and quantum groups Category theory and homological algebra Calculations on $\mathbb{C}^n$ Quick reference Bibliography Index of notation IndexReviewsAuthor InformationPramod N. Achar, Louisiana State University, Baton Rouge, LA. Tab Content 6Author Website:Countries AvailableAll regions |