Geodesic
Generalizations of the Cartan and Iwasawa Decompositions for SL2(k)
Journal of Lie theory, Tome 27 (2017) no. 1, pp. 155-176
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The Cartan and Iwasawa decompositions of real reductive Lie groups play a fundamental role in the representation theory of the groups and their corresponding symmetric spaces. These decompositions are defined by an involution with a compact fixed-point group, called a Cartan involution. For an arbitrary involution, one can consider similar decompositions. We offer a generalization of the Cartan and Iwasawa decompositions for algebraic groups defined over an arbitrary field k and a general involution.
Classification : 20G15
Mots-clés : Linear algebraic groups, Cartan decomposition, Iwasawa decomposition, generalized symmetric spaces 
@article{JLT_2017_27_1_JLT_2017_27_1_a7,
     author = {A. K. Sutherland},
     title = {Generalizations of the {Cartan} and {Iwasawa} {Decompositions} for {SL\protect\textsubscript{2}(k)}},
     journal = {Journal of Lie theory},
     pages = {155--176},
     year = {2017},
     volume = {27},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JLT_2017_27_1_JLT_2017_27_1_a7/}
}
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A. K. Sutherland. Generalizations of the Cartan and Iwasawa Decompositions for SL2(k). Journal of Lie theory, Tome 27 (2017) no. 1, pp. 155-176. http://geodesic.mathdoc.fr/item/JLT_2017_27_1_JLT_2017_27_1_a7/