Coverage of ordinary modules by computed cases at level −b

Ascertain whether all ordinary modules of the simple affine vertex algebra V_{-b}(g) are encompassed by the explicit computations provided in the paper at level −b.

Background

The abstract emphasizes that the explicit character computations at negative integral levels lead to broad coverage of modules; the authors state a global conjectural claim about completeness for ordinary modules at level −b.

The term “ordinary module” follows the standard vertex algebra usage (e.g., L_0-semisimple with finite-dimensional graded pieces). Confirming this claim would solidify the reach of the computed characters and their representation-theoretic consequences.

References

Conjecturally, all ordinary modules over V_{-b}(\mathfrak{g}) are covered by our computations.

— 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) (2401.06605 - Krylov et al., 12 Jan 2024) in Abstract