Characteristic-variety conjecture for the minimal automorphic sheaf

Let $\operatorname{Bun}_H$ be the stack of $H$-bundles, let ${\cal K}_H$ be the perverse sheaf constructed in the paper, and let ${\cal C}^0\subset T^*\operatorname{Bun}_H$ be the conic substack defined earlier in the paper. Characteristic-variety conjecture. The characteristic variety of ${\cal K}_H$ is ${\cal C}^0$, possibly with the zero section of $T^*\operatorname{Bun}_H\to\operatorname{Bun}_H$ added. This is a microlocal prediction for the sheaf realizing the minimal representation. The preceding arguments establish containment of ${\cal C}^0$ in the relevant characteristic varieties of local restrictions, but the stated global equality, including the possible zero section, remains conjectural.