Cohomological Induction and Unitary Representations (PMS-45), Volume 45 /

Cohomological Induction and Unitary Representations (PMS-45), Volume 45 / / David A. Vogan, Anthony W. Knapp.

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...

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Superior document:Title is part of eBook package: De Gruyter Princeton Mathematical Series eBook Package
VerfasserIn:
Knapp, Anthony W.,
Vogan, David A.,
Place / Publishing House:Princeton, NJ : : Princeton University Press, , [2016]
©1995
Year of Publication:2016
Language:English
Series:Princeton Mathematical Series ; 45
Online Access:
Physical Description:1 online resource (968 p.)
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100 1 |a Knapp, Anthony W.,   |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 0 |a Cohomological Induction and Unitary Representations (PMS-45), Volume 45 /  |c David A. Vogan, Anthony W. Knapp. 
264 1 |a Princeton, NJ :   |b Princeton University Press,   |c [2016] 
264 4 |c ©1995 
300 |a 1 online resource (968 p.) 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
347 |a text file  |b PDF  |2 rda 
490 0 |a Princeton Mathematical Series ;  |v 45 
505 0 0 |t Frontmatter --   |t CONTENTS --   |t PREFACE --   |t PREREQUISITES BY CHAPTER --   |t STANDARD NOTATION --   |t INTRODUCTION --   |t CHAPTER I. HECKE ALGEBRAS --   |t CHAPTER II. THE CATEGORY C(g, K) --   |t CHAPTER III. DUALITY THEOREM --   |t CHAPTER IV. REDUCTIVE PAIRS --   |t CHAPTER V. COHOMOLOGICAL INDUCTION --   |t CHAPTER VI. SIGNATURE THEOREM --   |t CHAPTER VII. TRANSLATION FUNCTORS --   |t CHAPTER VIII. IRREDUCIBILITY THEOREM --   |t CHAPTER IX. UNITARIZABILITY THEOREM --   |t CHAPTER X. MINIMAL K TYPES --   |t CHAPTER XI. TRANSFER THEOREM --   |t CHAPTER XII. EPILOG: WEAKLY UNIPOTENT REPRESENTATIONS --   |t APPENDIX A. MISCELLANEOUS ALGEBRA --   |t APPENDIX B. DISTRIBUTIONS ON MANIFOLDS --   |t APPENDIX C. ELEMENTARY HOMOLOGICAL ALGEBRA --   |t APPENDIX D. SPECTRAL SEQUENCES --   |t NOTES --   |t REFERENCES --   |t INDEX OF NOTATION --   |t INDEX 
506 0 |a restricted access  |u http://purl.org/coar/access_right/c_16ec  |f online access with authorization  |2 star 
520 |a 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. 
530 |a Issued also in print. 
538 |a Mode of access: Internet via World Wide Web. 
546 |a In English. 
588 0 |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) 
650 0 |a Harmonic analysis. 
650 0 |a Homology theory. 
650 0 |a Representations of groups. 
650 0 |a Semisimple Lie groups. 
650 7 |a MATHEMATICS / Algebra / Abstract.  |2 bisacsh 
653 |a Abelian category. 
653 |a Additive identity. 
653 |a Adjoint representation. 
653 |a Algebra homomorphism. 
653 |a Associative algebra. 
653 |a Associative property. 
653 |a Automorphic form. 
653 |a Automorphism. 
653 |a Banach space. 
653 |a Basis (linear algebra). 
653 |a Bilinear form. 
653 |a Cartan pair. 
653 |a Cartan subalgebra. 
653 |a Cartan subgroup. 
653 |a Cayley transform. 
653 |a Character theory. 
653 |a Classification theorem. 
653 |a Cohomology. 
653 |a Commutative property. 
653 |a Complexification (Lie group). 
653 |a Composition series. 
653 |a Conjugacy class. 
653 |a Conjugate transpose. 
653 |a Diagram (category theory). 
653 |a Dimension (vector space). 
653 |a Dirac delta function. 
653 |a Discrete series representation. 
653 |a Dolbeault cohomology. 
653 |a Eigenvalues and eigenvectors. 
653 |a Explicit formulae (L-function). 
653 |a Fubini's theorem. 
653 |a Functor. 
653 |a Gregg Zuckerman. 
653 |a Grothendieck group. 
653 |a Grothendieck spectral sequence. 
653 |a Haar measure. 
653 |a Hecke algebra. 
653 |a Hermite polynomials. 
653 |a Hermitian matrix. 
653 |a Hilbert space. 
653 |a Hilbert's basis theorem. 
653 |a Holomorphic function. 
653 |a Hopf algebra. 
653 |a Identity component. 
653 |a Induced representation. 
653 |a Infinitesimal character. 
653 |a Inner product space. 
653 |a Invariant subspace. 
653 |a Invariant theory. 
653 |a Inverse limit. 
653 |a Irreducible representation. 
653 |a Isomorphism class. 
653 |a Langlands classification. 
653 |a Langlands decomposition. 
653 |a Lexicographical order. 
653 |a Lie algebra. 
653 |a Linear extension. 
653 |a Linear independence. 
653 |a Mathematical induction. 
653 |a Matrix group. 
653 |a Module (mathematics). 
653 |a Monomial. 
653 |a Noetherian. 
653 |a Orthogonal transformation. 
653 |a Parabolic induction. 
653 |a Penrose transform. 
653 |a Projection (linear algebra). 
653 |a Reductive group. 
653 |a Representation theory. 
653 |a Semidirect product. 
653 |a Semisimple Lie algebra. 
653 |a Sesquilinear form. 
653 |a Sheaf cohomology. 
653 |a Skew-symmetric matrix. 
653 |a Special case. 
653 |a Spectral sequence. 
653 |a Stein manifold. 
653 |a Sub"ient. 
653 |a Subalgebra. 
653 |a Subcategory. 
653 |a Subgroup. 
653 |a Submanifold. 
653 |a Summation. 
653 |a Symmetric algebra. 
653 |a Symmetric space. 
653 |a Symmetrization. 
653 |a Tensor product. 
653 |a Theorem. 
653 |a Uniqueness theorem. 
653 |a Unitary group. 
653 |a Unitary operator. 
653 |a Unitary representation. 
653 |a Upper and lower bounds. 
653 |a Verma module. 
653 |a Weight (representation theory). 
653 |a Weyl character formula. 
653 |a Weyl group. 
653 |a Weyl's theorem. 
653 |a Zorn's lemma. 
653 |a Zuckerman functor. 
700 1 |a Vogan, David A.,   |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
773 0 8 |i Title is part of eBook package:  |d De Gruyter  |t Princeton Mathematical Series eBook Package  |z 9783110501063  |o ZDB-23-PMS 
773 0 8 |i Title is part of eBook package:  |d De Gruyter  |t Princeton University Press eBook-Package Archive 1927-1999  |z 9783110442496 
776 0 |c print  |z 9780691037561 
856 4 0 |u https://doi.org/10.1515/9781400883936 
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