The Springer theory is an important approach to the representation theory of Weyl groups or semisimple algebraic groups. In particular, it features so called Springer representations, which are associated to the unipotent conjugacy classes with an additional parameter, via so called Springer correspondence.
Kazhdan and Lusztig geometrically realized the Springer correspondence via the study of the Steinberg variety? placing its study within the geometric representation theory:
David Kazhdan, George Lusztig, A topological approach to Springer’s representations, Adv. in Math. 38 (1980), no. 2, 222–228 MR82f:20076 doi90005-5)
G. Lusztig, N. Spaltenstein, On the generalized Springer correspondence for classical groups, Advanced Studies in Pure Mathematics 6 (1985) 289–316.
N. Spaltenstein, On the generalized Springer correspondence for exceptional groups, Advanced Studies in Pure Mathematics 6 (1985) 317–338.
Ryoshi Hotta, On Springer’s representations, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 28 (1981), no. 3, 863–876 (1982) MR83h:20038
D. Clausen, Springer correspondence, Harvard thesis, pdf
Mikhail Grinberg, A generalization of Springer theory using nearby cycles, Represent. Theory 2 (1998), 410-431 pdf
Julia Sauter, A survey on Springer theory, arxiv/1307.0973
Gwyn Bellamy, Travis Schedler, Kostka polynomials from nilpotent cones and Springer fiber cohomology, arxiv/1509.02520
Some higher categorical aspects are more explicitly present in the works of Nadler and coworkers:
David Nadler, Springer theory via the Hitchin fibration, arxiv/0806.4566
David Ben-Zvi, David Nadler, Elliptic Springer theory, arxiv/1302.7053
Elements of the analogue of Springer theory for global fields are in
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