Classification of irreducible modules of W_3 algebra with c = -2
q-alg
2009-10-30 v1 High Energy Physics - Theory
Quantum Algebra
Abstract
We construct irreducible modules V_{\alpha}, \alpha \in \C over W_3 algebra with c = -2 in terms of a free bosonic field. We prove that these modules exhaust all the irreducible modules of W_3 algebra with c = -2. Highest weights of modules V_{\alpha}, \alpha \in \C with respect to the full (two-dimensional) Cartan subalgebra of W_3 algebra are (\alpha(\alpha -1)/2, \alpha(\alpha -1)(2\alpha -1)/6). They are parametrized by points (t, w) on a rational curve w^2 - t^2 (8t + 1)/9 = 0. Irreducible modules of vertex algebra W_{1+\infty} with c = -1 are also classified.
Keywords
Cite
@article{arxiv.q-alg/9708016,
title = {Classification of irreducible modules of W_3 algebra with c = -2},
author = {Weiqiang Wang},
journal= {arXiv preprint arXiv:q-alg/9708016},
year = {2009}
}
Comments
Latex, 22 pages