Cohomological Induction and Unitary Representations
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A01=Anthony W. Knapp
A01=David A. Vogan
Additive identity
Adjoint representation
Associative algebra
Author_Anthony W. Knapp
Author_David A. Vogan
Automorphic form
Automorphism
Basis (linear algebra)
Cartan subalgebra
Category=PBF
Category=PBPD
Classification theorem
Cohomology
Commutative property
Composition series
Conjugacy class
Conjugate transpose
Diagram (category theory)
Dimension (vector space)
Dirac delta function
Discrete series representation
Dolbeault cohomology
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Explicit formulae (L-function)
Fubini's theorem
Functor
Grothendieck group
Grothendieck spectral sequence
Haar measure
Hecke algebra
Hermite polynomials
Hermitian matrix
Hilbert space
Hilbert's basis theorem
Holomorphic function
Hopf algebra
Induced representation
Infinitesimal character
Invariant subspace
Invariant theory
Irreducible representation
Isomorphism class
Langlands classification
Langlands decomposition
Lie algebra
Matrix group
Parabolic induction
Penrose transform
Projection (linear algebra)
Reductive group
Representation theory
Semidirect product
Sesquilinear form
Sheaf cohomology
Skew-symmetric matrix
Special case
Spectral sequence
Subalgebra
Subcategory
Subgroup
Submanifold
Subquotient
Summation
Symmetrization
Theorem
Uniqueness theorem
Unitary operator
Unitary representation
Verma module
Weight (representation theory)
Weyl character formula
Weyl group
Weyl's theorem
Zorn's lemma
Zuckerman functor
Product details
- ISBN 9780691037561
- Weight: 1474g
- Dimensions: 152 x 235mm
- Publication Date: 21 May 1995
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Hardback
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This book offers a systematic treatment--the first in book form--of the development and use of cohomological induction to construct unitary representations. George Mackey introduced induction in 1950 as a real analysis construction for passing from a unitary representation of a closed subgroup of a locally compact group to a unitary representation of the whole group. Later a parallel construction using complex analysis and its associated co-homology theories grew up as a result of work by Borel, Weil, Harish-Chandra, Bott, Langlands, Kostant, and Schmid. Cohomological induction, introduced by Zuckerman, is an algebraic analog that is technically more manageable than the complex-analysis construction and leads to a large repertory of irreducible unitary representations of reductive Lie groups. The book, which is accessible to students beyond the first year of graduate school, will interest mathematicians and physicists who want to learn about and take advantage of the algebraic side of the representation theory of Lie groups.
Cohomological Induction and Unitary Representations develops the necessary background in representation theory and includes an introductory chapter of motivation, a thorough treatment of the "translation principle," and four appendices on algebra and analysis.
Anthony W. Knapp is Professor of Mathematics at the State University of New York at Stony Brook. David A. Vogan, Jr., is Professor of Mathematics at the Massachusetts Institute of Technology.
