论文标题
正交组的插值PBW变形
Interpolating PBW Deformations for the Orthosymplectic Groups
论文作者
论文摘要
我们建议使用插值类别研究PBW变形，并为正骨超级组证明了这一想法。我们采用基于合适的Jacobi身份的伪扫描和分区的组合演算，我们将PBW变形在（商的）插入式插值类别中分类。作为特殊情况，我们的分类恢复了Etingof-Gan-Ginzburg（2005）的无限Hecke代数家族，用于正交群体以及Tsymbaliuk（2015）的正交组以及其各自的标准表示，使用完全不同的几何学方法。我们的结果可以看作是将这些已知结果的扩展到所有正骨组的家族以及它们的所有基本表示，并通过新颖的插值技术来获得PBW变形。
We propose to use interpolation categories to study PBW deformations, and demonstrate this idea for the orthosymplectic supergroups. Employing a combinatorial calculus based on pseudographs and partitions which we derive from a suitable Jacobi identity, we classify PBW deformations in (quotients of) Deligne's interpolation categories for the orthosymplectic groups. As special cases, our classification recovers families of infinitesimal Hecke algebras found by Etingof-Gan-Ginzburg (2005) for the symplectic groups and by Tsymbaliuk (2015) for the orthogonal groups together with their respective standard representations using completely different geometric methods. Our results can be viewed as an extension of these known results to the family of all orthosymplectic groups together with all of their fundamental representations, obtained by novel interpolation techniques for PBW deformations.
