Subalgebras of $W_{1+\infty}$ and Their Quasifinite Representations
  We propose a series of new subalgebras of the $W_{1+\infty}$ algebra parametrized by polynomials $p(w)$, and study their quasifinite representations. We also investigate the relation between such subalgebras and the $\hat{\mbox{gl}}(\infty)$ algebra. As an example, we investigate the $\Win$ algebra which corresponds to the case $p(w)=w$, presenting its free field realizations and Kac determinants at lower levels. 
H.Awata, M.Fukuma, Y.Matsuo, S.Odake