We prove the simple-object prediction of Shan–Yan–Zhao and a basis-preserving dual-cell realization for the distinguished vacuum block of the simple affine vertex algebras , . The block has exactly simple objects, indexed by the subregular affine left cell containing . The proof combines a primitive-ideal inclusion, an independent exhaustion argument, and a finite-length step. A noncritical Sugawara lift supplies finite-dimensional weight-space detectors in the original Shan–Yan–Zhao category- block, so d'evissage applies to its ordinary Grothendieck group. We then identify this group, basis by basis, with the specialization of the corresponding dual affine left-cell module. An injective signed normalized-character realization identifies the resulting image with the canonical dual-cell image in the completed singular-orbit module and hence supplies the corresponding abstract -module structure. We do not identify this action with a functorial action arising from affine twisting functors or Kashiwara–Tanisaki localization. The subregular inverse Kazhdan–Lusztig calculation of Bezrukavnikov–Kac–Krylov also yields uniform character formulas.

生成讲解博客的中文版本

生成AI智能校验的中文版本