GENERICALLY FREE REPRESENTATIONS II: IRREDUCIBLE REPRESENTATIONS

We determine which faithful irreducible representationsVof a simple linear algebraic groupGare generically free for Lie(G), i.e., whichVhave an open subset consisting of vectors whose stabilizer in Lie(G) is zero. This relies on bounds on dimVobtained in prior work (part I), which reduce the problem to a finite number of possibilities forGand highest weights forV, but still infinitely many characteristics. The remaining cases are handled individually, some by computer calculation. These results were previously known for fields of characteristic zero, although new phenomena appear in prime characteristic; we provide a shorter proof that gives the result with very mild hypotheses on the characteristic. (The few characteristics not treated here are settled in part III.) These results are related to questions about invariants and the existence of a stabilizer in general position.