Abstract: The Kazhdan–Lusztig map was defined by Kazhdan and Lusztig in the 1980s, which maps a nilpotent orbit to a conjugacy class of the Weyl group. It has long been conjectured that the Kazhdan–Lusztig map is injective, and recently Yun confirmed this by constructing the minimal reduction map, which is a section of the Kazhdan–Lusztig map. In order to define the minimal reduction map, Yun showed that for general elements in the loop Lie algebra, the minimal reduction is unique. And he conjectured that the uniqueness of reduction holds for all topologically nilpotent regular semisimple elements. We prove this conjecture in the classical cases. In this talk, I will first recall the Kazhdan–Lusztig map and the minimal reduction map, and then explain our results and proofs with several examples. This talk is based on a joint work with Bin Wang and Yaoxiong Wen, available at arxiv.org/abs/2601.06744.