Would anyone be able to recommend text books that give an introduction to Geometric Representation Theory and survey papers that give an outline of the work that has been done in the field? I'm looking for references that would be suitable as a follow up to James Humphrey's "Linear Algebraic Groups" and a first year graduate Algebraic Geometry course. I'd also prefer the texts to be in English but if it's necessary, I could also read references in French.
Geometric Representation Theory – Introductory References
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Best Answer
I would encourage you to consider "Representation Theory and Complex Geometry" by Chriss and Ginzburg. In particular, I think you might enjoy the realization of irreducible representations of the Weyl group of a complex semisimple group $G$ on the Borel-Moore homology of the fibres of the Springer resolution of the nilpotent cone. For me, this has always been one of the motivating examples in geometric representation theory.