Twisted Teleman vanishing conjecture for twisted conformal blocks

Let $\mathfrak{g}$ be a Lie algebra with a standard automorphism $\sigma$, and let $D_{c,\sigma}$ and $D_c$ be the corresponding sets of dominant weights. For $\lambda,\mu\in D_{c,\sigma}$ and $\nu\in D_c$, let $V(\mu)^*$ denote the dual of the representation $V(\mu)$, and let $\mathscr{H}_c(\lambda)\otimes V(\nu)_1$ be the indicated module for $(t^{-1}\mathfrak{g}[t^{-1}])^\sigma$. Twisted Teleman vanishing conjecture. For every $i\geq 1$, the representation $V(\mu)^*$ does not occur in

$$H_i((t^{-1}\mathfrak{g}[t^{-1}])^\sigma,\mathscr{H}_c(\lambda)\otimes V(\nu)_1)$$

as a $\mathfrak{g}^\sigma$-representation. This conjecture is the twisted analogue of Teleman's vanishing theorem for conformal blocks; its validity is proposed here, and no resolution is supplied in the given text.