论文标题
McKay对应，共同厅代数和分类
McKay correspondence, cohomological Hall algebras and categorification
论文作者
论文摘要
令$π\ colon y \ to x $表示二维kleinian奇异性的规范分辨率$ x ADE类型。在本文中，我们在$ω$的同胞和K理论厅代数之间建立了同构，可与固定的坡度$ $ $ $ $ y $和$ζ$ quymemissistialsial-semissable-airmistional-dimentialsional的$ y $ $ y $相对$ $ $ $ $ $ $ $ $ $ $ $ $ $ undemiative $ conting $相对效率$相应地相应地相应地相差和$μ$。这些同构是由派生的McKay对应性诱导的。此外，它们被解释为相应分类的霍尔代数之间的单体等效版本的脱术版本。在A类案例中，我们提供了$ω$的共同体，k理论和分类的霍尔代数，可与$ y $相处的$ y $，固定的斜率$μ$：例如，在同胞案例中，可以用有限的yangians的Yangians表示有限的Ade Kadkin Diagrams Diagramians。
Let $π\colon Y\to X$ denote the canonical resolution of the two dimensional Kleinian singularity $X$ of type ADE. In the present paper, we establish isomorphisms between the cohomological and K-theoretical Hall algebras of $ω$-semistable properly supported sheaves on $Y$ with fixed slope $μ$ and $ζ$-semistable finite-dimensional representations of the preprojective algebra of affine type ADE of slope zero respectively, under some conditions on $ζ$ depending on the polarization $ω$ and $μ$. These isomorphisms are induced by the derived McKay correspondence. In addition, they are interpreted as decategorified versions of a monoidal equivalence between the corresponding categorified Hall algebras. In the type A case, we provide finer descriptions of the cohomological, K-theoretical and categorified Hall algebra of $ω$-semistable properly supported sheaves on $Y$ with fixed slope $μ$: for example, in the cohomological case, the algebra can be given in terms of Yangians of finite type ADE Dynkin diagrams.
