If U is the variety of unipotent elements in a reductive groupG, and X the variety of Borel subgroupsB, then the Springer resolution of U is the variety of pairs (u,B) of U×X such that u is in the Borel subgroup B. The map to U is the projection to the first factor. The Springer resolution for Lie algebras is similar, except that U is replaced by the nilpotent elements of the Lie algebra of G and X replaced by the variety of Borel subalgebras.[5]
The Grothendieck–Springer resolution is defined similarly, except that U is replaced by the whole group G (or the whole Lie algebra of G). When restricted to the unipotent elements of G it becomes the Springer resolution.[6][7]
^Ginzburg, Victor (1998), "Geometric methods in the representation theory of Hecke algebras and quantum groups", Representation theories and algebraic geometry (Montreal, PQ, 1997), NATO Advanced Science Institutes Series C: Mathematical and Physical Sciences, vol. 514, Kluwer Acad. Publ., Dordrecht, pp. 127–183, arXiv:math/9802004, Bibcode:1998math......2004G, ISBN0-7923-5193-2, MR1649626