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Seminar in Representation Theory

On the Springer correspondence for wreath products

  • Date : 2024/05/16 (Thu.) 11:00~12:00
  • Location : Seminar Room 638, Institute of Mathematics (NTU Campus)
  • Speaker : You-Hung Hsu (Academia Sinica)
  • Organizer : Cheng-Chiang Tsai (Academia Sinica)
  • Abstract : In this talk, we present a study of the wreath products of two symmetric groups from a geometric perspective. We proved that they are so-called generalized Weyl groups in the sense of Iwahori's generalized Tits system, and hence it leads to a Bruhat decomposition whose cells are indexed by such groups, which are not Coxeter groups in general. We further provide geometric realizations of their group algebras in terms of the top Borel-Moore homology of certain Steinberg varieties. Consequently, we obtain a new Springer correspondence for wreath products, as a geometric counterpart of the (algebraic) Clifford theory. In particular, we obtain a new Springer correspondence of type B/C/D using only type A geometry. This is a joint work with C.J. Lai.