3 problems

Let $G$ be a reductive group with Borel subgroup $B$, unipotent radical $U$, maximal torus $T=B/U$, and quotient map $\pi:G\to G/U$. Let $\Phi_{G,\rho,\psi}$ be the $\rho$-Bessel s…

Let $G$ be a reductive group over $\mathbb F_q$, let $\rho$ be a representation as in the Braverman–Kazhdan construction, and let $\Phi_{G,\rho,\psi}$ be the corresponding $\rho$-B…

Let $G$ be an algebraic group with Frobenius endomorphism $F$, and let $\rho^\flat$ be a morphism satisfying the assumptions specified in the source. Let $\phi^G_\rho$ be the centr…