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

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

1994-06-17

arxiv.org/abs/hep-th/9406111v1

J.Phys.A28:105-112,1995

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1088/0305-4470/28/1/015

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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