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arXiv · hep-th/9406111

Subalgebras of $W_{1+\infty}$ and Their Quasifinite Representations

H. Awata·M. Fukuma·Y. Matsuo·S. Odake
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Abstract

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.

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H. Awata, M. Fukuma, Y. Matsuo, S. Odake. 1994-06-17. Subalgebras of $W_{1+\infty}$ and Their Quasifinite Representations. https://doi.org/10.1088/0305-4470%2F28%2F1%2F015

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