Representations of Real and P-Adic Groups

The Institute for Mathematical Sciences at the National University of Singapore hosted a research program on “Representation Theory of Lie Groups” from July 2002 to January 2003. As part of the program, tutorials for graduate students and junior researchers were given by leading experts in the field. This invaluable volume collects the expanded lecture notes of those tutorials. The topics covered include uncertainty principles for locally compact abelian groups, fundamentals of representations of p-adic groups, the Harish–Chandra–Howe local character expansion, classification of the square-integrable representations modulo cuspidal data, Dirac cohomology and Vogan's conjecture, multiplicity-free actions and Schur–Weyl–Howe duality. The lecturers include Tomasz Przebinda from the University of Oklahoma, USA; Gordan Savin from the University of Utah, USA; Stephen DeBacker from Harvard University, USA; Marko Tadić from the University of Zagreb, Croatia; Jing-Song Huang from The Hong Kong University of Science and Technology, Hong Kong; Pavle Pandǽić from the University of Zagreb, Croatia; Chal Benson and Gail Ratcliff from East Carolina University, USA; and Roe Goodman from Rutgers University, USA. Contents:Three Uncertainty Principles for an Abelian Locally Compact Group (T Przebinda)Lectures on Representations of p-Adic Groups (G Savin)Lectures on Harmonic Analysis for Reductive p-Adic Groups (S DeBacker)On Classification of Some Classes of Irreducible Representations of Classical Groups (M Tadić)Dirac Operators in Representation Theory (J-S Huang & P Pandǽić)On Multiplicity-Free Actions (C Benson & G Ratcliff)Multiplicity-Free Spaces and Schur–Weyl–Howe Duality (R Goodman) Readership: Graduate students and researchers in the areas of representation theory, harmonic analysis and invariant theory. Keywords:Representation Theory;p-Adic Groups;Real Reductive Groups;Unitary Representations;Multiplicity-Free Actions