SIMPLE WEAK MODULES FOR THE FIXED POINT SUBALGEBRA OF THE HEISENBERG VERTEX OPERATOR ALGEBRA OF RANK 1 BY AN AUTOMORPHISM OF ORDER 2 AND WHITTAKER VECTORS.

Let M(1) be the vertex operator algebra with the Virasoro element ω associated to the Heisenberg algebra of rank 1 and let M(1)+ be the subalgebra of M(1) consisting of the fixed points of an automorphism of M(1) of order 2. We classify the simple weak M(1)+-modules with a non-zero element w such that for some integer s ≥ 2, ωiw ∈ ℂw (i = [s/2] + 1, [s/2] + 2, ..., s -- 1), ωsw ∈ ℂx w, and ωiw = 0 for all i > s. The result says that any such simple weak M(1)+-module is isomorphic to some simple weak M(1)-module or to some θ-twisted simple weak M(1)-module. [ABSTRACT FROM AUTHOR]