A Survey on Springer Theory

Understand

This is not standard in the sense that we understand a Springer map to be a collapsing of homogeneous bundles.

• Apart from that we use mostly techniques from Chriss and Ginzbergs book but we work in the equivariant derived category of Bernstein and Lunts.
• We define Steinberg algebras as (equivariant) Borel-Moore homology algebras of the associated Steinberg varieties.
• The data of the BBD-decomposition theorem applied to the Springer map give a parametrization of projective graded and simple graded modules over the Steinberg algebra.