Construction
Several approaches to Springer correspondence have been developed. T. A. Springer's original construction (1976) proceeded by defining an action of W on the top-dimensional l-adic cohomology groups of the algebraic variety Bu of the Borel subgroups of G containing a given unipotent element u of a semisimple algebraic group G over a finite field. This construction was generalized by Lusztig (1981), who also eliminated some technical assumptions. Springer later gave a different construction (1978), using the ordinary cohomology with rational coefficients and complex algebraic groups.
Kazhdan and Lusztig found a topological construction of Springer representations using the Steinberg variety and, allegedly, discovered Kazhdan–Lusztig polynomials in the process. Generalized Springer correspondence has been studied by Lusztig-Spaltenstein (1985) and by Lusztig in his work on character sheaves. Borho and MacPherson (1983) gave yet another construction of the Springer correspondence.
Read more about this topic: Springer Correspondence
Famous quotes containing the word construction:
“There is, I think, no point in the philosophy of progressive education which is sounder than its emphasis upon the importance of the participation of the learner in the formation of the purposes which direct his activities in the learning process, just as there is no defect in traditional education greater than its failure to secure the active cooperation of the pupil in construction of the purposes involved in his studying.”
—John Dewey (1859–1952)
“There’s no art
To find the mind’s construction in the face.”
—William Shakespeare (1564–1616)
“Striving toward a goal puts a more pleasing construction on our advance toward death.”
—Mason Cooley (b. 1927)