Noncommutative Counterparts of the Springer Resolution
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 algebrogeometric 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 April 2006
 DOI:
 10.48550/arXiv.math/0604445
 arXiv:
 arXiv:math/0604445
 Bibcode:
 2006math......4445B
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Algebraic Geometry
 EPrint:
 ICM talk