Symmetric k-varieties are a generalization of symmetric spaces to general fields. Orbits of a minimal parabolic k-subgroup acting on a symmetric k-variety are essential in the study of symmetric k-varieties and their representations. In this article, we present the classification of these orbits for the group SL(2,k) for a number of base fields k, including finite fields and the -adic numbers. We use the characterization in Helminck and Wang (199314. Helminck , A. G. , Wang , S. P. ( 1993 ). On rationality properties of involutions of reductive groups . Adv. Math. 99 ( 1 ): 26 - 96 .[CrossRef], [Web of Science ®]View all references), which requires one to first classify the orbits of the θ-stable maximal k-split tori under the action of the k-points of the fixed point group.View full textDownload full textKey Words k-split tori, Minimal parabolic subgroups, p-adic numbers, Symmetric k-varieties, Symmetric spaces2000 Mathematics Subject Classification68Q40, 20G15, 20G20, 22E15, 22E46, 43A85Related var addthis_config = { ui_cobrand: "Taylor & Francis Online", services_compact: "citeulike,netvibes,twitter,technorati,delicious,linkedin,facebook,stumbleupon,digg,google,more", pubid: "ra-4dff56cd6bb1830b" }; Add to shortlist Link Permalink http://dx.doi.org/10.1080/00927870802466983
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