Harish-Chandra modules for semisimple Lie groups with one conjugacy class of Cartan subgroups

1992 ◽  
pp. 75-111 ◽  
Author(s):  
David H. Collingwood ◽  
Ronald S. Irving
Keyword(s):  
Conjugacy Class ◽  
Lie Groups ◽  
Semisimple Lie Groups ◽  
Cartan Subgroups

On Some q-Analogs of a Theorem of Kostant-Rallis

2000 ◽  
Vol 52 (2) ◽  
pp. 438-448 ◽  
Author(s):  
N. R. Wallach ◽  
J. Willenbring
Keyword(s):  
Conjugacy Class ◽  
Quantum Computation ◽  
Lie Groups ◽  
Lie Algebra ◽  
Lie Group ◽  
Cartan Subgroup ◽  
Semisimple Lie Groups ◽  
Semisimple Lie Group ◽  
Real Group ◽  
Qubit States

AbstractIn the first part of this paper generalizationsof Hesselink’s q-analog of Kostant’smultiplicity formula for the action of a semisimple Lie group on the polynomials on its Lie algebra are given in the context of the Kostant-Rallis theorem. They correspond to the cases of real semisimple Lie groups with one conjugacy class of Cartan subgroup. In the second part of the paper a q-analog of the Kostant-Rallis theorem is given for the real group SL(4, ) (that is SO(4) acting on symmetric 4 × 4 matrices). This example plays two roles. First it contrasts with the examples of the first part. Second it has implications to the study of entanglement of mixed 2 qubit states in quantum computation.

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
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