In 1987, Chen Zhijie studied a particular irreducible 16-dimensional module V for the general linear group over an algebraically closed field k of characteristic 3. Chen's interest in this module stemmed from the analysis of prehomogeneous vector spaces in prime characteristic. These are representations which have a dense orbit in the underlying vector space (considered as an affine variety). Such representations were studied extensively in characteristic 0 in [SK]. Chen showed that V is a prehomogeneous vector space for which has a relative invariant (cf. [Z]) of degree 8. The set of vectors at which this invariant takes a nonzero value is the dense orbit. Having a dense orbit in V is a necessary condition for a linear algebraic group over an algebraically closed field (such as ) to have finitely many orbits in V.
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