Softcover ISBN: | 978-2-85629-918-0 |
Product Code: | AST/417 |
List Price: | $60.00 |
AMS Member Price: | $48.00 |
Softcover ISBN: | 978-2-85629-918-0 |
Product Code: | AST/417 |
List Price: | $60.00 |
AMS Member Price: | $48.00 |
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Book DetailsAstérisqueVolume: 417; 2020; 177 ppMSC: Primary 22; 20; 17
The authors present an algorithm for the computation of irreducible unitary representations of a real reductive Lie group \(G\). The Langlands classification, as formulated by Knapp and Zuckerman, presents any Hermitian representation as being the deformation of a unitary representation occurring in the Plancherel formula. The behavior of these deformations is partly determined by the Kazhdan-Lusztig analysis of the irreducible characters; more complete information comes from Beilinson-Bernstein proof of Jantzen's conjectures.
The authors' algorithm traces through this deformation the changes in the signature of the form that can occur at the points of reducibility. An important tool is a variant of Weyl's “unitary trick”: The authors replace the classic Hermitian form (for which Lie\((G)\) acts by antisymmetric operators) by a new Hermitian form (for which it is a compact form of Lie \((G)\) which acts by antisymmetric operators).
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
ReadershipGraduate students and research mathematicians.
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The authors present an algorithm for the computation of irreducible unitary representations of a real reductive Lie group \(G\). The Langlands classification, as formulated by Knapp and Zuckerman, presents any Hermitian representation as being the deformation of a unitary representation occurring in the Plancherel formula. The behavior of these deformations is partly determined by the Kazhdan-Lusztig analysis of the irreducible characters; more complete information comes from Beilinson-Bernstein proof of Jantzen's conjectures.
The authors' algorithm traces through this deformation the changes in the signature of the form that can occur at the points of reducibility. An important tool is a variant of Weyl's “unitary trick”: The authors replace the classic Hermitian form (for which Lie\((G)\) acts by antisymmetric operators) by a new Hermitian form (for which it is a compact form of Lie \((G)\) which acts by antisymmetric operators).
A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.
Graduate students and research mathematicians.