Noncommutative Counterparts of the Springer Resolution
Roman Bezrukavnikov
Abstract
Springer resolution of the set of nilpotent elements in a semisimple Lie algebra plays a central role in geometric representation theory. A new structure on this variety has arisen in several representation theoretic constructions, such as the (local) geometric Langlands duality and modular representation theory. It is also related to some algebro-geometric problems, such as the derived equivalence conjecture and description of T. Bridgeland's space of stability conditions. The structure can be described as a noncommutative counterpart of the resolution, or as a t-structure on the derived category of the resolution. The intriguing fact that the same t-structure appears in these seemingly disparate subjects has strong technical consequences for modular representation theory.
Create a lesson
Related papers
On silting theory for complete path algebras
Maximilian Kaipel, Daniel Labardini-Fragoso, Håvard Utne Terland
Geometrization of Kottwitz-Shelstad transfer and Vogan's conjecture on local Arthur packets
Clifton Cunningham, Alexander Hazeltine, Baiying Liu et al.
Hammock coordinates for silting subcategories of derived-discrete algebras
Shantanu Sardar
Representations of Bound Quivers over F1 and Hall Algebras
Changjian Fu, Xuelian Xiao
Closed energy formulas on tensor squares of perfect crystals of types D4(3) and G2(1)
Shaolong Han
Generalized parabolic Demazure modules and the N!/2-conjecture for two-row diagrams
Anton Khoroshkin, Ievgen Makedonskyi