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

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.

arXiv comment10 pages, LaTeX, RIMS-985, YITP/K-1076, YITP/U-94-22, SULDP-1994-4

References in corpus (5)

• Quasifinite highest weight modules over the Lie algebra of differential operators on the circle
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Cited by in corpus (3)

• Determinant and Character of W-infinity algebra
• Finite growth representations of infinite Lie conformal algebras
• Quasifinite Representations of Classical Lie subalgebras of $W_{\infty ,p}$