nLab
Springer correspondence

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.

  • wikipedia Springer correspondence
  • T. A. Springer, A construction of representations of Weyl groups, Invent. Math. 44 (1978), no. 3, 279–293 MR0491988 doi
  • N. Chriss, V. Ginzburg, Representation theory and complex geometry, Birkhäuser 1997. x+495 pp.

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:

Elements of the analogue of Springer theory for global fields are in

  • Zhiwei Yun, Towards a Global Springer Theory I: The affine Weyl group action, arxiv/0810.2146

Last revised on September 10, 2015 at 06:55:55. See the history of this page for a list of all contributions to it.