The Steinberg Variety and Representations of Reductive Groups
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We give an overview of some of the main results in geometric representation theory that have been proved by means of the Steinberg variety. Steinberg's insight was to use such a variety of triples in order to prove a conjectured formula by Grothendieck.
The Steinberg variety was later used to give an alternative approach to Springer's representations and played a central role in the proof of the Deligne-Langlands conjecture for Hecke algebras by Kazhdan and Lusztig.
37 pages; significant revision and extension; to appear in J. Algebra
37 pages; significant revision and extension; to appear in J. Algebra