Minimal reduction type in classical cases

Abstract

We prove Yun's minimal reduction conjecture for all classical groups. More precisely, for any topologically nilpotent regular semisimple element $\gamma$, we show that the associated minimal reduction set $\mathrm{RT}_{\mathrm{min}}(\gamma)$ consists of a single nilpotent orbit. This result confirms and extends Yun's earlier work in types A and C, and resolves the remaining cases in types B and D. Moreover, we provide an explicit and effective procedure for determining $\mathrm{RT}_{\mathrm{min}}(\gamma)$.