Journal of Lie Theory 27 (2017), No. 1, 155--176
Copyright Heldermann Verlag 2017
Generalizations of the Cartan and Iwasawa Decompositions for SL2(k)
Amanda K. Sutherland
Dept. of Mathematical Sciences, Shenandoah University, 1460 University Drive, Winchester, VA 22601, U.S.A.
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.
Keywords: Linear algebraic groups, Cartan decomposition, Iwasawa decomposition, generalized symmetric spaces.
[ Fulltext-pdf (349 KB)] for subscribers only.