7 problems

Let $\mathbb{G}$ be a generic group, let $e,m>0$, and let $(\mathbb{L},\lambda)$ and $(\mathbb{M},\mu)$ be respectively $\Phi_e$- and $\Phi_m$-cuspidal pairs. Let the intersection…

Let $\mathbb{G}$ be a generic finite reductive group, and let $e,m>0$ with corresponding $\Phi_e$- and $\Phi_m$-cuspidal pairs. Consider the intersection of the two Harish–Chandra…

Let $({\mathbf{L}},\lambda)$ and $({\mathbf{M}},\mu)$ be $e$-pairs of ${\mathbf{G}}$. Write $({\mathbf{L}},\lambda)\leq_e({\mathbf{M}},\mu)$ when ${\mathbf{L}}\leq{\mathbf{M}}$ and…

Deligne–Lusztig parabolic-independence conjecture. The maps ${\mathbf{R}}_{{\mathbf{L}}\leq{\mathbf{P}}}^{\mathbf{G}}$ and…

Harish–Chandra compatibility conjecture. The maps from irreducible characters of the normalizer to Calogero–Moser fixed points, from those characters to unipotent representations v…

Let $G$ be a finite reductive group, let $L_0$ be a Levi subgroup, and let $X_0$ be a $kL_0^F$-module. Consider the Harish–Chandra series of $(L_0,X_0)$ and a $kG^F$-module in that…

Let $G$ be a finite reductive group with connected center, let $L_0$ be a Levi subgroup, and let $X_0$ be a $kL_0^F$-module defining a Harish–Chandra series. For a proper split Lev…