Classification of irreducible modules of W3 algebra with c = -2
Abstract
We construct irreducible modules Vα, α ∈ over W3 algebra with c = -2 in terms of a free bosonic field. We prove that these modules exhaust all the irreducible modules of W3 algebra with c = -2. Highest weights of modules Vα, α ∈ with respect to the full (two-dimensional) Cartan subalgebra of W3 algebra are (α(α -1)/2, α(α -1)(2α -1)/6). They are parametrized by points (t, w) on a rational curve w2 - t2 (8t + 1)/9 = 0. Irreducible modules of vertex algebra W1+∞ with c = -1 are also classified.
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