
Journal of Lie Theory 12 (2002), No. 1, 301304 Copyright Heldermann Verlag 2002 A Note on Observable Subgroups of Linear Algebraic Groups and a Theorem of Chevalley Nazih Nahlus Dept. of Mathematics, American University of Beirut, c/o New York Office, 850 Third Ave. 18th floor, New York, NY 100226297, U.S.A. Let H be an algebraic subgroup of a linear algebraic group G over an algebraically closed field K. We show that H is observable in G if and only if there exists a finitedimensional rational Gmodule V and an element v of V such that H is the isotropy subgroup of v as well as the isotropy subgroup of the line Kv. Moreover, we give a similar result in the case where H contains a normal algebraic subgroup A which is observable in G. In this case, we deduce that H is observable in G whenever H/A has non nontrivial rational characters. We also give an example from complex analytic groups. [ Fulltextpdf (113 KB)] 