Langlands Classification and Irreducible Characters for Real Reductive Groups

This monograph explores the geometry of the local Langlands conjecture. The conjecture predicts a parametrizations of the irreducible representations of a reductive algebraic group over a local field in terms of the complex dual group and the Weil-Deligne group. For p-adic fields, this conjecture has not been proved; but it has been refined to a detailed collection of (conjectural) relationships between p-adic representation theory and geometry on the space of p-adic representation theory and geometry on the space of p-adic Langlands parameters. In the case of real groups, the predicted parametrizations of representations was proved by Langlands himself. Unfortunately, most of the deeper relations suggested by the p-adic theory (between real representation theory and geometry on the space of real Langlands parameters) are not true. The purposed of this book is to redefine the space of real Langlands parameters so as to recover these relationships; informally, to do "Kazhdan-Lusztig theory on the dual group". The new definitions differ from the classical ones in roughly the same way that Delignea?s definition of a Hodge structure differs from the classical one. This book provides and introduction to some modern geometric methods in representation theory. It is addressed to graduate students and research workers in representation theory and in automorphic forms.Adams, J. is the author of 'Langlands Classification and Irreducible Characters for Real Reductive Groups ', published 1992 under ISBN 9780817636340 and ISBN 081763634X.