Braverman–Kazhdan's acyclicity conjecture for gamma sheaves

Let $G$ be a reductive group, let $B$ be a Borel subgroup with unipotent radical $U$, and let $\Psi_{G,\rho}$ be the gamma sheaf associated with a representation $\rho$ of the dual group. Consider the quotient map

$$\pi_U:G\rightarrow G/U.$$

Braverman–Kazhdan's acyclicity conjecture. The object $(\pi_U)_!\Psi_{G,\rho}$ is supported on $T=B/U\subset G/U$. Equivalently, for every $g\in G-B$,

$$H^*_c(gU,i^*\Psi_{G,\rho})=0,$$

where $i:gU\rightarrow G$ is the inclusion. This vanishing property implies the induction part of the preceding conjecture. The abstract says that the paper proves the corresponding Braverman–Kazhdan conjecture in the de Rham setting.