Unitary Representations of Reductive Lie Groups
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A01=David A. Vogan
Abelian group
Annihilator (ring theory)
Atiyah-Singer index theorem
Author_David A. Vogan
Automorphic form
Cartan subgroup
Category=PBF
Class function (algebra)
Classification theorem
Cohomology
Commutator subgroup
Dimension (vector space)
Discrete series representation
Dixmier conjecture
Duality (mathematics)
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Exponential map (Lie theory)
Exponential map (Riemannian geometry)
Exterior algebra
Function space
Group homomorphism
Harmonic analysis
Hecke algebra
Hilbert space
Holomorphic function
Holomorphic vector bundle
Homomorphism
Induced representation
Inner automorphism
Invariant subspace
Irreducible representation
Isometry group
K-finite
Lie algebra
Lie algebra cohomology
Lie algebra representation
Lie group
Mathematical induction
Maximal compact subgroup
Minkowski space
Parabolic induction
Principal homogeneous space
Principal series representation
Pseudo-Riemannian manifold
Pullback (category theory)
Ramanujan-Petersson conjecture
Reductive group
Regularity theorem
Representation of a Lie group
Representation theorem
Representation theory
Riemannian manifold
Schwartz space
Semisimple Lie algebra
Sheaf (mathematics)
Sign (mathematics)
Spectral theory
Subgroup
Support (mathematics)
Symplectic geometry
Symplectic group
Symplectic vector space
Theorem
Topological group
Unitary group
Unitary matrix
Unitary representation
Universal enveloping algebra
Vector bundle
Weyl algebra
Weyl character formula
Zariski's main theorem
Zonal spherical function
Product details
- ISBN 9780691084824
- Weight: 454g
- Dimensions: 152 x 229mm
- Publication Date: 21 Oct 1987
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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This book is an expanded version of the Hermann Weyl Lectures given at the Institute for Advanced Study in January 1986. It outlines some of what is now known about irreducible unitary representations of real reductive groups, providing fairly complete definitions and references, and sketches (at least) of most proofs. The first half of the book is devoted to the three more or less understood constructions of such representations: parabolic induction, complementary series, and cohomological parabolic induction. This culminates in the description of all irreducible unitary representation of the general linear groups. For other groups, one expects to need a new construction, giving "unipotent representations." The latter half of the book explains the evidence for that expectation and suggests a partial definition of unipotent representations.
