K-Theory and Representation Theory

Detailed lecture notes covering applications of C*-algebras and K-theory to the representation theory of reductive real and p-adic groups.

This book provides a tool-kit for the advanced study of symmetry, one of the most important concepts in mathematics and physics. Full of detailed examples, it discusses some of the most exciting interactions between operator algebras and representation theory, at a level suited to PhD students and young researchers.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.