中央研究院數學研究所

Seminar in Representation Theory

On the Springer correspondence for wreath products

2024/05/16 (Thu.) 11:00~12:00

日期 : 2024/05/16 (Thu.) 11:00~12:00
地點 : 中研院數學所 638研討室 (台大校區)
主講人 : 許佑鴻 (本所)
籌辦人 : 蔡政江 (本所)
演講摘要 : 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.