Local Langlands and Springer correspondences (Q2283637)

In this expository paper, the author provides a detailed overview of the recent results on the local Langlands correspondence for reductive \(p\)-adic groups, which predicts an extrodinary connection between irreducible representations of reductive \(p\)-adic groups and the Langlands parameters. We note that the Langlands parameters are certain analogs of Galois representations. In these notes, the author focuses on the joint work with Moussaoui and Solleveld and its links with the generalized Springer correspondence. Relations with the so-called ABPS conjecture, due to Baum, Plymen, Solleveld, and the author are also discussed. Notes contain a detailed introduction, many definitions, interesting illustrative examples and a discussion of certain conjectures. In the course of her exposition, the author provides a nice survey of studied topic, including definitions of some more basic notions as the Weil group, the \(L\)-group, etc. Therefore this nicely written paper is to be recommended to non-experts as well as experts on the field. For the entire collection see [Zbl 1414.11004].