Leseprobe
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Cohomological Induction and Unitary Representations (PMS-45), Volume 45
David A. Vogan, Anthony W. Knapp
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
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.
Kundenbewertungen
Diagram (category theory), Irreducible representation, Weyl's theorem, Associative algebra, Theorem, Unitary representation, Dimension (vector space), Weyl group, Functor, Subgroup, Automorphism, Symmetrization, Lie algebra, Composition series, Haar measure, Reductive group, Discrete series representation, Sheaf cohomology, Cartan subalgebra, Classification theorem, Summation, Subalgebra, Penrose transform, Submanifold, Automorphic form, Hermitian matrix, Langlands classification, Hecke algebra, Langlands decomposition, Sesquilinear form, Infinitesimal character, Conjugate transpose, Basis (linear algebra), Cohomology, Subquotient, Explicit formulae (L-function), Uniqueness theorem, Hilbert space, Hilbert's basis theorem, Induced representation, Zuckerman functor, Unitary operator, Representation theory, Zorn's lemma, Grothendieck group, Invariant theory, Commutative property, Spectral sequence, Weight (representation theory), Grothendieck spectral sequence, Isomorphism class, Adjoint representation, Dirac delta function, Additive identity, Matrix group, Special case, Weyl character formula, Hopf algebra, Subcategory, Conjugacy class, Holomorphic function, Skew-symmetric matrix, Dolbeault cohomology, Invariant subspace, Projection (linear algebra), Semidirect product, Hermite polynomials, Fubini's theorem, Verma module, Parabolic induction