Harmonic Analysis and Representations of Semisimple Lie Groups: Lectures Given at the NATO Advanced Study Institute on Representations of Lie Groups and Harmonic Analysis, Held at Liège, Belgium, September 5–17, 1977Joseph Albert Wolf, M. Cahen, M. de Wilde Springer Netherlands, 1980 M07 31 - 495 páginas This book presents the text of the lectures which were given at the NATO Advanced Study Institute on Representations of Lie groups and Harmonic Analysis which was held in Liege from September 5 to September 17, 1977. The general aim of this Summer School was to give a coordinated intro duction to the theory of representations of semisimple Lie groups and to non-commutative harmonic analysis on these groups, together with some glance at physical applications and at the related subject of random walks. As will appear to the reader, the order of the papers - which follows relatively closely the order of the lectures which were actually give- follows a logical pattern. The two first papers are introductory: the one by R. Blattner describes in a very progressive way a path going from standard Fourier analysis on IR" to non-commutative harmonic analysis on a locally compact group; the paper by J. Wolf describes the structure of semisimple Lie groups, the finite-dimensional representations of these groups and introduces basic facts about infinite-dimensional unitary representations. Two of the editors want to thank particularly these two lecturers who were very careful to pave the way for the later lectures. Both these chapters give also very useful guidelines to the relevant literature. |
Contenido
Introduction | 3 |
Locally compact Abelian groups | 10 |
Compact groups | 19 |
Derechos de autor | |
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Términos y frases comunes
a₁ adjoint algebra g automorphism Banach representation Cartan subalgebra Cartan subgroup commutative complete COROLLARY corresponding decomposition define deformation denote direct sum discrete series representations element Enright equivalent exists exp TH finite finite-dimensional formula functor g-module g₁ group G h₁ Haar measure Harish-Chandra module Hence highest weight Hilbert space homomorphism infinitesimal character invariant eigendistribution irreducible representation isomorphism lattice Lemma Let G Lie algebra linear M₁ Math Moreover multiplicity n₁ nilpotent nonzero P-dominant integral P₁ Plancherel measure polynomial positive root positive system proof properties PROPOSITION prove real form representation of G resp result root system Section semisimple Lie groups simple root subgroup of G subset subspace Suppose symmetric theorem topology type II(2 unique unitary representation V₁ V₂ Verma modules weight module weight vector Weyl group