Dualizing complexes on the moduli of parabolic bundles

For a non-archimedean local field $F$ and a connected reductive group $G$ over $F$ equipped with a parabolic subgroup $P$, we show that the dualizing complex on ${\mathrm{B}\mathrm{u}\mathrm{n}}_P$, the moduli stack of $P$-bundles on the Fargues–Fontaine curve, can be described explicitly in terms of the modulus character of $P$. As applications, we identify various characters appearing in the theory of local and global Shimura varieties, show the Harris–Viehmann conjecture in the Hodge–Newton reducible case, and carry out some computations of the geometric Eisenstein functors for general parabolics.