Algorithmic testing for dense orbits of Borel subgroups

Let G be a reductive algebraic group, B a Borel subgroup of G and U the unipotent radical of B. Let it = Lie(U) be the Lie algebra of U and it a B-submodule of it. In this note we discuss the algorithm Dense Orbits of Borel Subgroups (DOOBS) which determines whether B acts on it with a dense orbit. We have programmed DOOBS in GAP4 and used it to classify all instances when B acts on it with a dense orbit for G of sermisimple rank at most 8 and char k zero or good for G. So in particular, we have the classification for G of exceptional type. © 2004 Elsevier B.V. All rights reserved.