REPRESENTATIONS AND CHARACTERS

This volume offers a comprehensive exploration of the representation theory of reductive groups over local fields, with emphasis on characters, matrix coefficients, branching laws, and the Weil representation. It brings together a collection of expository lecture notes and original research contributions that highlight both the historical foundations of the subject and the most recent advances in the field.

Designed for graduate students, postdoctoral fellows, and young researchers, the book combines accessible introductions to advanced concepts with state-of-the-art results from leading experts including Anne-Marie Aubert, Roger Howe, and Toshiyuki Kobayashi. It serves both as an entry point to modern representation theory and as a reference for specialists seeking current perspectives.

Originating from the international conference Representations and Characters: Revisiting the Works of Harish-Chandra and André Weil — a satellite event of the Virtual ICM 2022, organized by the Institute for Mathematical Sciences, National University of Singapore, from July 1st to 16th — this volume collects some key research themes from this major meeting and makes them accessible to a wider mathematical audience.

Contents:

• Foreword
• Preface
• Correspondences between Affine Hecke Algebras and Applications (Anne-Marie Aubert)
• Progresses on the Local Gan–Gross–Prasad Conjecture (Cheng Chen)
• Symmetry Breaking for PGL(2) over Non-Archimedean Local Fields (Corina Ciobotaru and Jan Frahm)
• Invariant Vectors for Depth Zero Supercuspidals of GSp(4) (Jonathan Cohen)
• Overview on the Theory of Double Flag Varieties for Symmetric Pairs (Lucas Fresse and Kyo Nishiyama)
• On Local Character Expansions for Principal Series Representations of General Linear Groups (Maxim Gurevich)
• Projection of Elliptic Orbits and Branching Laws (Hongyu He)
• Mathematics around the Heisenberg Group (Roger Howe)
• Proper Actions and Representation Theory (Toshiyuki Kobayashi)

Readership: Graduate students, young researchers, and specialists in modern representation theory of reductive groups over local fields.