Reductive groups, the loop Grassmannian, and the Springer resolution
Reductive groups, the loop Grassmannian, and the Springer resolution
复制标题
还原群、循环格拉斯曼和施普林格解析
DOI：
--
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
S. Riche
中科院分区：
文献类型：
--
作者：
Pramod N. Achar;S. Riche
在本文中，我们证明了与特征 p 大于 Coxeter 数的代数闭域上连通的还原代数群的表示类别的块的派生类别和施普林格分辨率（或抛物线对应物）上的等变相干滑轮的派生类别有关的类别的等价性。就主块而言，结合之前的结果，这为 Lusztig 量子群在统一根上提供了由 Arkhipov-Bezrukavnikov-Ginzburg 著名构造的模块化版本。作为应用，我们证明了 Finkelberg-Mirković 猜想的“分级版本”，该猜想用对偶仿射格拉斯曼上的混合反常滑轮来描述主块，并推导出 Lusztig 猜想的大特征的新证明。
In this paper we prove equivalences of categories relating the derived category of a block of the category of representations of a connected reductive algebraic group over an algebraically closed field of characteristic p bigger than the Coxeter number and a derived category of equivariant coherent sheaves on the Springer resolution (or a parabolic counterpart). In the case of the principal block, combined with previous results, this provides a modular version of celebrated constructions due to Arkhipov–Bezrukavnikov–Ginzburg for Lusztig’s quantum groups at a root of unity. As an application, we prove a “graded version” of a conjecture of Finkelberg–Mirković describing the principal block in terms of mixed perverse sheaves on the dual affine Grassmannian, and deduce a new proof of Lusztig’s conjecture in large characteristic.
舒伯特微积分和扭转爆炸
影响因子：
3.9
作者：
G. Williamson
通讯作者：
G. Williamson