论文标题
小量子组和弹簧分辨率的支持理论
Support theory for the small quantum group and the Springer resolution
论文作者
论文摘要
我们考虑了小量子组U_Q（g），对于几乎简单的代数g，在复数中几乎是尺寸的g组，并且是一个足够大的统一Q的根。我们表明，A型小量子组的Balmer频谱允许从（Projectivized）Springer分辨率的连续陈述p（ñ）\ to（stab u_q（g））。该陈述被证明是光谱中密集的开放子集的同态性。在类型A_1中，我们精确地计算了Balmer频谱，其中显示为项目活动的Nilpotent锥。我们的结果扩展到任意Dynkin类型，为小量子鲍尔提供了某些猜想。在本文的结论中，我们涉及与几何表示理论和对数TQFTS的关系，如Arkhipov-Bezrukavnikov-Ginzburg和Schweigert所做的作品所示。
We consider the small quantum group u_q(G), for an almost-simple algebraic group G over the complex numbers and a root of unity q of sufficiently large order. We show that the Balmer spectrum for the small quantum group in type A admits a continuous surjection P(Ñ) \to Spec(stab u_q(G)) from the (projectivized) Springer resolution. This surjection is shown to be a homeomorphism over a dense open subset in the spectrum. In type A_1 we calculate the Balmer spectrum precisely, where it is shown to be the projectivized nilpotent cone. Our results extend to arbitrary Dynkin type provided certain conjectures hold for the small quantum Borel. At the conclusion of the paper we touch on relations with geometric representation theory and logarithmic TQFTs, as represented in works of Arkhipov-Bezrukavnikov-Ginzburg and Schweigert-Woike respectively.
