Lusztig's Jordan decomposition and a finite field instance of relative Langlands duality

Zhicheng Wang

Lusztig \cite{L5,L6} gave a parametrization for $\mathrm{Irr}({\mathrm{G}}^{\mathrm{F}})$, where $G$ is a reductive algebraic group defined over ${\mathbb{F}}_q$, with Frobenius map $F$. This parametrization…