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Unitary Representations of Real Reductive Groups
 
Jeffrey D. Adans University of Maryland, College Park, MD
Marc A. A. van Leeuwen Laboratoire de Mathëmatiques et Applications, Université de Poitiers, France
Peter E. Trapa University of Utah, Salt Lake City, UT
David A. Vogan Massachusetts Institute of Technology, Cambridge, MA
A publication of the Société Mathématique de France
Unitary Representations of Real Reductive Groups
Softcover ISBN:  978-2-85629-918-0
Product Code:  AST/417
List Price: $60.00
AMS Member Price: $48.00
Please note AMS points can not be used for this product
Unitary Representations of Real Reductive Groups
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Unitary Representations of Real Reductive Groups
Jeffrey D. Adans University of Maryland, College Park, MD
Marc A. A. van Leeuwen Laboratoire de Mathëmatiques et Applications, Université de Poitiers, France
Peter E. Trapa University of Utah, Salt Lake City, UT
David A. Vogan Massachusetts Institute of Technology, Cambridge, MA
A publication of the Société Mathématique de France
Softcover ISBN:  978-2-85629-918-0
Product Code:  AST/417
List Price: $60.00
AMS Member Price: $48.00
Please note AMS points can not be used for this product
  • Book Details
     
     
    Astérisque
    Volume: 4172020; 177 pp
    MSC: 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.

    Readership

    Graduate students and research mathematicians.

  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 4172020; 177 pp
MSC: 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.

Readership

Graduate students and research mathematicians.

Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.