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.
This book mainly discusses the representation theory of the special linear group 8L(2, 1R), and some applications of this theory. In fact the emphasis is on the applications; the working title of the book while it was being writ ten was "Some Things You Can Do with 8L(2). " Some of the applications are outside representation theory, and some are to representation theory it self. The topics outside representation theory are mostly ones of substantial classical importance (Fourier analysis, Laplace equation, Huyghens' prin ciple, Ergodic theory), while the ones inside representation theory mostly concern themes that have been central to Harish-Chandra's development of harmonic analysis on semisimple groups (his restriction theorem, regularity theorem, character formulas, and asymptotic decay of matrix coefficients and temperedness). We hope this mix of topics appeals to nonspecialists in representation theory by illustrating (without an interminable prolegom ena) how representation theory can offer new perspectives on familiar topics and by offering some insight into some important themes in representation theory itself. Especially, we hope this book popularizes Harish-Chandra's restriction formula, which, besides being basic to his work, is simply a beautiful example of Fourier analysis on Euclidean space. We also hope representation theorists will enjoy seeing examples of how their subject can be used and will be stimulated by some of the viewpoints offered on representation-theoretic issues.
This handbook provides an evidence-based approach to common obstetrics & gynaecological problems faced by O & G clinicians and general practitioners in their daily practice. It is the only book available with current evidence-based recommendations and protocols in O & G.Compiled by experienced experts, this new edition contains 24 new chapters. The existing chapters have been updated using the latest evidence. The authors have included multiple flow charts and detailed practical approaches to various gynaecology and obstetric issues. The book will be a valuable and quick practical guide to everyone — not only to general practitioners and O & G clinicians, but also to medical students and resident doctors. Topics like “Approach to Ectopic Pregnancy” and “Pelvic Inflammatory Disease” will provide invaluable guidance to even emergency medicine doctors.
This practical guide provides an up-to-date and concise account of many obstetric and gynaecological conditions based on evidence-based medicine. The 50 topics covered include menstrual disorders, abnormal PAP smears, ovarian cysts, subfertility, vaginal discharge, contraception and hormonal replacement therapy, pregnancy and its complications as well as common obstetrics and gynaecology (O&G) investigations.The book includes the use of flow charts to simplify the description of investigations and treatments of the various common conditions in obstetrics and gynaecology. This is particularly useful for doctors in the primary healthcare setting in their day-to-day clinical practice. It also contains criteria for referral to OBGYN doctors. It will also serve as an essential guide for medical students and nursing staff and a handy summary for OBGYN specialists.
This invaluable volume collects the expanded lecture notes of thosetutorials. The topics covered include uncertainty principles forlocally compact abelian groups, fundamentals of representations of"p"-adic groups, the Harish?Chandra?Howe local characterexpansion, classification of the square-integrable representationsmodulo cuspidal data, Dirac cohomology and Vogan's conjecture, multiplicity-free actions and Schur?Weyl?Howe duality.
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