Symmetry is one of the most important concepts in mathematics and physics. Emerging from the 2021 LMS-Bath Summer School, this book provides Ph.D. students and young researchers with some of the essential tools for the advanced study of symmetry. Illustrated with numerous examples, it explores some of the most exciting interactions between Dirac operators, K-theory and representation theory of real reductive groups. The final chapter provides a self-contained account of the representation theory of p-adic groups, from the very basics to an advanced perspective, with many arithmetic aspects.
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Detailed lecture notes covering applications of C*-algebras and K-theory to the representation theory of reductive real and p-adic groups.
List of contributors; Preface;
1. Group C*-algebras, C*-correspondences
and K-Theory Bram Mesland and Mehmet Haluk engün;
2. Tempered
representations of semisimple Lie groups Peter Hochs;
3. Dirac operators and
representation theory Hang Wang;
4. Representation theory of p-adic reductive
groups Anne-Marie Aubert; Index.
Roger Plymen is Emeritus Professor at Manchester University and Visiting Professor at Southampton University. He recently published 'The Great Prime Number Race' (2020). His paper from 1983, The Dirac Operator and the Principal Series for Complex Semisimple Lie Groups, co-authored by Michael G. Penington, was a springboard for several of the developments in this book. Mehmet Haluk engün is Senior Lecturer at University of Sheffield. Originally from Istanbul, Dr. engün's mathematical trajectory took him to Madison, Essen, Barcelona, Bonn, Warwick and finally Sheffield. An algebraic number theorist by training, Dr. engün's recent research has focused on bringing tools and ideas from C*-algebras and Noncommutative Geometry to the theory of automorphic forms and the Langlands Programme.
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