2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/172292We 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. AlgebraRepresentation TheoryK-Theory and Homology22E46, 19L47, 20G05 (Primary); 14F99, 20G99 (Secondary)text