Harmonic analysis on semisimple Lie groups
Reads0
Chats0
TLDR
In this article, it was shown that for any representation x, VT and ©^ depend only on the class co of 7r, and that tr 4̂ is actually independent of the choice of this base.Abstract:
Then tr 4̂ is actually independent of the choice of this base. Let VT denote the set of a l l /G^ i (G) such that ir(f) is of the trace class. Then Vr is a linear subspace of Li(G). Put 0 . ( / ) = tr *•(ƒ) ( f £ F T ) . Then ®T is a linear function on VT which we may call the character of 7T. Of course this concept would be useful only when the space V* is fairly large. Let 8(G) denote the set of all equivalence classes of irreducible unitary representations of G. It is easy to see that for any representation x, VT and ©^ depend only on the class co of 7r. Hence we may de-read more
Citations
More filters
Book
The Convenient Setting of Global Analysis
Andreas Kriegl,Peter W. Michor +1 more
TL;DR: Calculus of smooth mappings Calculus of holomorphic and real analytic mappings Partitions of unity Smoothly real compact spaces Extensions and liftings of mappings Infinite dimensional manifolds Calculus on infinite dimensional manifold, infinite dimensional differential geometry Manifolds of Mappings Further applications References as mentioned in this paper.
Book
C*-Algebras and Finite-Dimensional Approximations
TL;DR: In this article, the authors present a classification of group von Neumann algebras based on the following properties: weak expectation property, local lifting property, and local reflexivity.
Book
Representation of Lie groups and special functions
A. U. Klimyk,N. Ya. Vilenkin +1 more
TL;DR: The theory of elliptic integrals was introduced by Abel as discussed by the authors, who proposed a special function to evaluate integrals, which is called integral sine, logarithm, exponential function, probability integral and so on.
Journal ArticleDOI
A duality for symmetric spaces with applications to group representations
TL;DR: In this paper, the authors propose a reduction to the Hermitian Hyperbolic case and derive the Conical Functions and Finite-Dimensional Representations of X and S.
References
More filters
Book
Théorie des distributions
TL;DR: The merite as discussed by the authors is a date marque une date dans le progres des mathematiques and de la physique en levant l'ambiguite que constituait le succes des methodes de calcul symbolique aupres des physiciens and l'inacceptabilite de leurs formules au regard de la rigueur mathematiques.
Journal ArticleDOI
Groupes Réductifs
Armand Borel,Jacques Tits +1 more
TL;DR: In this paper, the authors present conditions générales d'utilisation (http://www.numdam.org/conditions), i.e., Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
Journal ArticleDOI
Discrete series for semisimple Lie groups. II: Explicit determination of the characters
BookDOI
Automorphic forms on semisimple lie groups
Harish-Chandra,J. G. M. Mars +1 more
TL;DR: In this article, the automorphic forms on semisimple lie groups is one book that we really recommend you to read, to get more solutions in solving this problem.
Journal ArticleDOI