Coulomb Branch Student Seminar | The Kazhdan-Lusztig Map for so(8)

Abstract

We introduce the notion of Kazhdan-Lusztig map for simple Lie algebras. It assigns for each nilpotent orbit a conjugacy class of the Weyl group. We also construct Lusztig's map, for which the Kazhdan-Lusztig map is its canonical section. We focus on the case so(8). We review the nilpotent orbits and compute the conjugacy classes of the Weyl group of so(8), then we compute explicitly the Kazhdan-Lusztig map for so(8) and give necessary explanations.