Quasifinite representations of classical Lie subalgebras of $W_{\bm\infty ,\,p}$W∞,p
Quasifinite representations of classical Lie subalgebras of $W_{\bm\infty ,\,p}$W∞,p
We show that there are exactly two anti-involution $\sigma_{\pm}$ of the algebra of differential operators on the circle that are a multiple of $p(t\partial_t)$ preserving the principal gradation ($p\in\CC[x]$ non-constant). We classify the irreducible quasifinite highest weight representations of the central extension $\hat{\D}_p^{\pm}$ of the Lie subalgebra fixed by $-\sigma_{\pm}$. …