Intersection Cohomology and Character Sheaves
Lusztig (1985) replaced the ℓ-adic cohomology used to define the Deligne-Lusztig representations with intersection ℓ-adic cohomology, and introduced certain perverse sheaves called character sheaves. The representations defined using intersection cohomology are related to those defined using ordinary cohomology by Kazhdan–Lusztig polynomials. The F-invariant irreducible character sheaves are closely related to the irreducible characters of the group GF.
Read more about this topic: Deligne–Lusztig Theory
Famous quotes containing the words intersection, character and/or sheaves:
“You can always tell a Midwestern couple in Europe because they will be standing in the middle of a busy intersection looking at a wind-blown map and arguing over which way is west. European cities, with their wandering streets and undisciplined alleys, drive Midwesterners practically insane.”
—Bill Bryson (b. 1951)
“Crime seems to change character when it crosses a bridge or a tunnel. In the city, crime is taken as emblematic of class and race. In the suburbs, though, it’s intimate and psychological—resistant to generalization, a mystery of the individual soul.”
—Barbara Ehrenreich (b. 1941)
“Being young you have not known
The fool’s triumph, nor yet
Love lost as soon as won,
Nor the best labourer dead
And all the sheaves to bind.”
—William Butler Yeats (1865–1939)