Proof of the Hard Lefschetz Theorem
In this chapter, we outline the proof of Soergel’s conjecture via versions of the hard Lefschetz theorem and Hodge–Riemann bilinear relations.
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Ben Elias Shotaro Makisumi Ulrich Thiel Geordie Williamson
Introduction to Soergel bimodules
RSME Springer Series Volume 5
Editor-in-Chief José Bonet, Instituto Universitario de Matemática Pura y Aplicada (IUMPA), Universitat Politècnica de València, Valencia, Spain Series Editors Nicolas Andruskiewitsch, FaMAF - CIEM (CONICET), Universidad Nacional de Córdoba, Córdoba, Argentina María Emilia Caballero, Instituto de Matemáticas, Universidad Nacional Autónoma de México, México, México Pablo Mira, Departamento de Matematica Aplicada y Estadistica, Universidad Politécnica de Cartagena, Cartagena, Spain Timothy G. Myers, Centre de Recerca Matemàtica, Barcelona, Spain Marta Sanz-Solé, Department of Mathematics and Informatics, Barcelona Graduate School of Mathematics (BGSMath), Universitat de Barcelona, Barcelona, Spain Karl Schwede, Department of Mathematics, University of Utah, Salt Lake City, USA
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Ben Elias • Shotaro Makisumi • Ulrich Thiel • Geordie Williamson
Introduction to Soergel Bimodules
Ben Elias Department of Mathematics University of Oregon, Fenton Hall Eugene, OR, USA
Shotaro Makisumi Department of Mathematics Columbia University New York, NY, USA
Ulrich Thiel Department of Mathematics University of Kaiserslautern Kaiserslautern, Germany
Geordie Williamson School of Mathematics and Statistics University of Sydney Sydney, Australia
ISSN 2509-8888 ISSN 2509-8896 (electronic) RSME Springer Series ISBN 978-3-030-48825-3 ISBN 978-3-030-48826-0 (eBook) https://doi.org/10.1007/978-3-030-48826-0 © The Editor(s) (if applicable) and The Author(s), under exclusive licence to Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective law