5 problems

Let $G_{\mathbb{R}}$ be a real reductive group. Let $\Pi_u(G_{\mathbb{R}})$ be the set of equivalence classes of irreducible unitary $G_{\mathbb{R}}$-representations, and let…

Orbit-method compatibility conjecture. We have

Let $G_{\mathbb R}$ be the real points of a connected reductive algebraic group, and let $\mathsf{Cov}^{i\mathbb R}(G_{\mathbb R})$ denote the real co-adjoint covers of…

Let $\mathfrak g$ be one of $V\!ir$, $W$, or $W_{\geq -1}$. For a local function $\chi\in\mathfrak g^*$, choose a polarization and form the annihilator of the induced module; write…

Let $G$ be a complex simple Lie group with Lie algebra $\mathfrak{g}$, and let $K$ be a maximal compact subgroup of $G$ with complexification $K_{\mathbb{C}}$. For a nilpotent orbi…