Fourier transforms of some invariant distribution on semisimple Lie groups and Lie algebras

1979 ◽  
pp. 1-7 ◽  
Author(s):  
Dan Barbasch
Keyword(s):  
Lie Groups ◽  
Lie Algebras ◽  
Fourier Transforms ◽  
Invariant Distribution ◽  
Semisimple Lie Groups

scholarly journals Representations of complex semisimple Lie groups and Lie algebras

1966 ◽  
Vol 72 (3) ◽  
pp. 522-526 ◽  
Author(s):  
K. R. Parthasarathy ◽  
R. Ranga Rao ◽  
V. S. Varadarajan
Keyword(s):  
Lie Groups ◽  
Lie Algebras ◽  
Semisimple Lie Groups ◽  
Complex Semisimple

scholarly journals Some Questions about Semisimple Lie Groups Originating in Matrix Theory

2003 ◽  
Vol 46 (3) ◽  
pp. 332-343 ◽  
Author(s):  
Dragomir Ž. Ðoković ◽  
Tin-Yau Tam
Keyword(s):  
Partial Order ◽  
Lie Groups ◽  
Lie Algebras ◽  
Matrix Theory ◽  
Compact Subgroup ◽  
Orbit Space ◽  
Natural Partial Order ◽  
Semisimple Lie Groups ◽  
Complex Matrix ◽  
Semisimple Complex

AbstractWe generalize the well-known result that a square traceless complex matrix is unitarily similar to a matrix with zero diagonal to arbitrary connected semisimple complex Lie groups G and their Lie algebras under the action of a maximal compact subgroup K of G. We also introduce a natural partial order on : x ≤ y if f (K · x) ⊆ f (K · y) for all f 2 *, the complex dual of . This partial order is K-invariant and induces a partial order on the orbit space /K. We prove that, under some restrictions on , the set f (K · x) is star-shaped with respect to the origin.

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