# Denominator identity for Lie superalgebras

Let $$\mathfrak g$$ be a basic classic simple Lie superalgebra.

Fix a maximal isotropic subset $$S \subset \Delta$$ and choose a set of simple roots $$\Pi$$ containing $$S$$. Let $$R$$ be the Weyl denominator for the corresponding triangular decomposition. The following Weyl denominator identity was suggested by Kac and Wakimoto and is proved here:

$$R e^{\rho} = \sum_{w \in W^{\#}} sgn(w) w \Big(\frac{e^{\rho}}{\prod_{\beta \in S} (1+e^{-\beta})}\Big)$$

In the denominator identity, we have sum over the Weyl group $$W^{\#}$$ which is the Weyl group of the “bigger” irreducible root system part of the root system of $$\mathfrak g_0$$. My question is, what are the white vertices of the Dynkin diagram of $$\mathfrak g$$ whose associated simple reflections generate $$W^{\#}$$?.