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^{\#}$ ?.