Twisted Spin Verlinde dimension formula

Let $m\geq 3$, and let $SC_m\rightarrow SL(V)$ be a representation satisfying the condition in. Write $d_V$ for the height (Dynkin index) of $V$, and let $N_{d_V}^{+}$ and $N_{d_V}^{-}$ denote the corresponding integral and half-integral twisted Verlinde numbers. Twisted Spin Verlinde conjecture. One has

$$h^0({\cal M}^{-}({\rm Spin}_m),\Theta(V))=(-1)^m\bigl(N_{d_V}^{+}-N_{d_V}^{-}\bigr).$$

This refines the conjecture cited by the authors for the twisted moduli space and extends the expected Verlinde-type identity to both even and odd $m$; the supplied text does not indicate whether it has been proved or remains open.