The subtop cohomology conjecture for metaplectic Whittaker models

Let $\rho$ be the quadratic form on the coweight lattice associated with the metaplectic data. For $\bar c$ the residue-field point and $\bar\theta$ the image of $\theta$ in the adjoint coweight lattice, let $\theta$ range over simple coroots. Assume

$$\varrho(\alpha_i)\notin \mathbb{Z}$$

for every simple coroot $\alpha_i$. The subtop cohomology property is the condition that, for every positive coweight $\lambda$ that is not a simple coroot, the compactly supported cohomology complex

$$\operatorname{R\Gamma}_c(\operatorname{Gr}_B^0\cap \operatorname{Gr}_{B^-}^{-\lambda},s_{-\lambda}^*\mathcal L_G)$$

is concentrated in degrees at most $\langle\lambda,2\check\rho\rangle-2$. Subtop cohomology conjecture. If $\varrho(\alpha_i)\notin\mathbb{Z}$ for every simple coroot $\alpha_i$, then the subtop cohomology property is satisfied for $\varrho$. The property is used to control the subtop cohomology of metaplectic Whittaker sheaves; the supplied text gives no resolution status beyond this asserted statement.