Leseprobe
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Unitary Representations of Reductive Lie Groups. (AM-118), Volume 118
David A. Vogan
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
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.
Kundenbewertungen
Unitary matrix, Semisimple Lie algebra, Induced representation, Irreducible representation, Sheaf (mathematics), Dixmier conjecture, Hilbert space, Schwartz space, Atiyah–Singer index theorem, Cartan subgroup, Unitary group, Group homomorphism, Reductive group, Exterior algebra, Lie algebra cohomology, Abelian group, Principal series representation, Pseudo-Riemannian manifold, Theorem, Automorphic form, Exponential map (Riemannian geometry), Mathematical induction, Minkowski space, Sign (mathematics), Zonal spherical function, Holomorphic vector bundle, Annihilator (ring theory), Spectral theory, K-finite, Maximal compact subgroup, Invariant subspace, Vector bundle, Discrete series representation, Function space, Principal homogeneous space, Classification theorem, Regularity theorem, Symplectic group, Unitary representation, Harmonic analysis, Homomorphism, Topological group, Duality (mathematics), Inner automorphism, Representation of a Lie group, Commutator subgroup, Dimension (vector space), Lie algebra representation, Holomorphic function, Subgroup, Weyl character formula, Weyl algebra, Lie group, Representation theorem, Riemannian manifold, Support (mathematics), Symplectic vector space, Exponential map (Lie theory), Parabolic induction, Class function (algebra), Hecke algebra, Lie algebra, Universal enveloping algebra, Cohomology, Isometry group, Symplectic geometry, Ramanujan–Petersson conjecture, Representation theory, Pullback (category theory), Zariski's main theorem