Overview
- Unique comprehensive resource available on Soergel bimodules in book form
- First account in book form of diagrammatics for Soergel bimodules, with hundreds of figures
- Contains hundreds of exercises and examples to help the reader learn the material
Part of the book series: RSME Springer Series (RSME, volume 5)
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Table of contents (27 chapters)
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Front Matter
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The Classical Theory of Soergel Bimodules
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Front Matter
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Historical Context: Category O $$\mathcal {O}$$ and the Kazhdan–Lusztig Conjectures
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Front Matter
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Historical Context: Category O and the Kazhdan–Lusztig Conjectures
Keywords
About this book
This book provides a comprehensive introduction to Soergel bimodules. First introduced by Wolfgang Soergel in the early 1990s, they have since become a powerful tool in geometric representation theory. On the one hand, these bimodules are fairly elementary objects and explicit calculations are possible. On the other, they have deep connections to Lie theory and geometry. Taking these two aspects together, they offer a wonderful primer on geometric representation theory. In this book the reader is introduced to the theory through a series of lectures, which range from the basics, all the way to the latest frontiers of research.
This book serves both as an introduction and as a reference guide to the theory of Soergel bimodules. Thus it is intended for anyone who wants to learn about this exciting field, from graduate students to experienced researchers.
Reviews
Authors and Affiliations
About the authors
Ben Elias hails from sunny Massachusetts and is well known for his wit and ability to do diagrammatic calculations like no other. He’s also been known to solve a crossword at the same time as playing a Bach prelude. He is currently a professor at the University of Oregon.
Shotaro Makisumi (known to his friends as “Macky”) is originally from Ube, Japan. He studied at Stanford and is currently at Columbia. Despite his successes proving theorems, he is still best known for his extraordinary skills with the Rubik’s Cube.
Ulrich Thiel studied in Kaiserslautern, Germany, and after a brief voyage around the globe, recently returned there to take up a professorship. Let’s be honest: he’s the brains behind the operation.
Geordie Williamson grew up with the wombats and kangaroos in rural Australia. He completed his PhD under Soergel’s supervision, and after stints in Oxford and Bonn, returned to his furry friends in 2017.
All four authors delight in challenging each other to bouts of sumo, before retiring to a traditional meal of chanko nabe.Bibliographic Information
Book Title: Introduction to Soergel Bimodules
Authors: Ben Elias, Shotaro Makisumi, Ulrich Thiel, Geordie Williamson
Series Title: RSME Springer Series
DOI: https://doi.org/10.1007/978-3-030-48826-0
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
Hardcover ISBN: 978-3-030-48825-3Published: 27 September 2020
Softcover ISBN: 978-3-030-48828-4Published: 28 September 2021
eBook ISBN: 978-3-030-48826-0Published: 26 September 2020
Series ISSN: 2509-8888
Series E-ISSN: 2509-8896
Edition Number: 1
Number of Pages: XXV, 588
Number of Illustrations: 290 b/w illustrations, 181 illustrations in colour
Topics: Algebra, Group Theory and Generalizations, Category Theory, Homological Algebra, Topological Groups, Lie Groups, Geometry, Algebraic Geometry