Geodesic
On Some $q$ -Analogs of a Theorem of Kostant-Rallis
Canadian journal of mathematics, Tome 52 (2000) no. 2, pp. 438-448

Voir la notice de l'article provenant de la source Cambridge University Press

In the first part of this paper generalizations of 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 $\text{SL(4,}\,\mathbb{R}\text{)}$ (that is $\text{SO}(4)$ 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.
DOI : 10.4153/CJM-2000-020-0
Mots-clés : 22E47, 20G05 
Wallach, N. R.; Willenbring, J. On Some $q$ -Analogs of a Theorem of Kostant-Rallis. Canadian journal of mathematics, Tome 52 (2000) no. 2, pp. 438-448. doi: 10.4153/CJM-2000-020-0
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     journal = {Canadian journal of mathematics},
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