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We extend the techniques in arXiv:2209.08865(1) to the non-simply-lacedsituation, and calculate explicit special values of parabolic affine inverseKazhdan-Lusztig polynomials for subregular nilpotent orbits. We thus obtainexplicit character formulas for certain irreducible representations of affineLie algebras. As particular cases, we compute characters of simple vertexalgebras $V_{k}(\mathfrak{g})$ for $k=-1,\ldots,-b$, where $b$ is the largestlabel of the highest short coroot $\theta^\vee$. Conjecturally, all ordinarymodules over $V_{-b}(\mathfrak{g})$ are covered by our computations. As anapplication, we obtain the explicit formulas for flavoured Schur indices ofrank one Argyres-Douglas 4d SCFTs with flavour symmetry $G_2$ and $B_3$. Ourresults are proved using the geometry of the Springer resolution. We identifythe cell quotient of the anti-spherical module over $\widehat{W}$ correspondingto the subregular cell with a certain one-dimensional extension of a moduledefined by Lusztig. We describe the canonical basis in this modulegeometrically and present an explicit description of the corresponding objectsin the derived category of equivariant coherent sheaves on the Springerresolution. They correspond to irreducible objects in the heart of a certain$t$-structure that we describe using an equivariant version of the derivedMcKay correspondence.

Affine Kazhdan-Lusztig polynomials on the subregular cell in non  simply-laced Lie algebras: with an application to character formulae (with an  appendix by Roman Bezrukavnikov, Vasily Krylov, and Kenta Suzuki)