H. Awata et al., SUBALGEBRAS OF W-1+INFINITY AND THEIR QUASIFINITE REPRESENTATIONS, Journal of physics. A, mathematical and general, 28(1), 1995, pp. 105-112
We propose a series of new subalgebras of the W-1+infinity algebra par
ametrized by polynomials p(w), and study their quasifinite representat
ions. We also investigate the relation between such subalgebras and th
e gl(infinity) algebra. As an example, we investigate the W-infinity,
algebra which corresponds to the case p(w) = w, presenting its free fi
eld realizations and Kac determinants at lower levels.