次正则仿射胞与D型-1级顶点代数
Subregular affine cells and the level $-1$ vertex algebra of type $D$
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中文总结 AI 辅助
该研究证明了Shan-Yan-Zhao仿射左胞猜想对$\ell\ge5$的$L_{-1}(D_\ell)$成立，明确真空块单对象数量，推导了Grothendieck群的特殊化及统一特征标公式。
中文摘要 AI 辅助
我们证明了Shan-Yan-Zhao仿射左胞猜想对简单仿射顶点代数$L_{-1}(D_\ell)$（$\ell\ge5$）成立。特殊的真空块恰有$\ell+1$个单对象，由包含$s_0$的次正则仿射左胞索引。证明用到两个有限维要素：本原理想包含表明预测的非真空模降至相关商，另一穷尽论证排除了更多最高权。由此得Grothendieck群是对应对偶仿射左胞模的$q=1$特殊化，该等同还给出用次正则逆Kazhdan-Lusztig系数表示的统一特征标公式。
英文摘要
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 $L_{-1}(D_\ell)$, $\ell\ge5$. The block has exactly $\ell+1$ simple objects, indexed by the subregular affine left cell containing $s_0$. 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-$\mathcal O$ block, so dévissage applies to its ordinary Grothendieck group. We then identify this group, basis by basis, with the $q=1$ 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 $\widehat W$-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.
发表机构
- Sichuan University（四川大学）
机构由 AI 辅助整理，请以论文原文为准。
