The Steinberg Variety and Representations of Reductive Groups

Details The Steinberg Variety and Representations of Reductive Groups The Steinberg Variety and Representations of Reductive Groups

2008-02-06

arxiv.org/abs/0802.0764v4

Mathematics

Representation Theory

37 pages; significant revision and extension; to appear in J. Algebra

Scientific paper

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.

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