In mathematics, Deligne–Lusztig theory is a way of constructing linear representations of finite groups of Lie type using ℓ-adic cohomology with compact support, introduced by Deligne & Lusztig (1976).
Lusztig (1984) used these representations to find all representations of all finite simple groups of Lie type.
Read more about Deligne–Lusztig Theory: Motivation, Deligne–Lusztig Varieties, Properties of Deligne–Lusztig Characters, Lusztig's Classification of Irreducible Characters, Examples, Intersection Cohomology and Character Sheaves
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