EMIS ELibM Electronic Journals Journal of Lie Theory
Vol. 12, No. 1, pp. 301--304 (2002)

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Note on Observable Subgroups of Linear Algebraic Groups

Nazih Nahlus

Nazih Nahlus
Department of Mathematics
American University of Beirut
c/o New York Office
850 Third Ave. 18th floor
New York, New York 10022-6297

Abstract: 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 finite-dimensional rational G-module 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 non-trivial rational characters. We also give an example from complex analytic groups.

Classification (MSC2000): Primary 20G05, 20G15, 22E45

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Electronic fulltext finalized on: 30 Oct 2001. This page was last modified: 9 Nov 2001.

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