  The bc\beta\gamma-system W of rank 3 has an action of the affine vertex
algebra V_0(sl_2), and the commutant vertex algebra C =Com(V_0(sl_2), W)
contains copies of V_{-3/2}(sl_2) and Odake's algebra O. Odake's algebra is an
extension of the N=2 superconformal algebra with c=9, and is generated by eight
fields which close nonlinearly under operator product expansions. Our main
result is that V_{-3/2}(sl_2) and O form a Howe pair (i.e., a pair of mutual
commutants) inside C. More generally, any finite-dimensional representation of
a Lie algebra g gives rise to a similar Howe pair, and this example corresponds
to the adjoint representation of sl_2.
