000			02143 a2200277 4500
003			OSt
005			20220510150338.0
008			220509b xxu||||| |||| 00| 0 eng d
020			_a9780691037561
040			_cIIT Kanpur
041			_aeng
082			_a512.55 _bK727c
100			_aKnapp, Anthony W.
245			_aCohomological induction and unitary representations _cAnthony W. Knapp and David A. Vogan
260			_bPrinceton University Press _c1995 _aPrinceton
300			_axvii, 948p
440			_aPrinceton Mathematical series
490			_a/ edited by Luis A. Caffarelli, John N. Mather and Elias M. Stein ; 45
520			_aThis 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.
650			_aSemisimple Lie groups
650			_aRepresentations of groups
650			_aHomology theory
650			_aHarmonic analysis
700			_aVogan, David A.
942			_cBK
999			_c565372 _d565372