14 problems

Let $G$ be an almost algebraic group, let $H$ be a closed algebraic subgroup, and let $\mathfrak{g}$ and $\mathfrak{h}$ be their Lie algebras, with duals $\mathfrak{g}^*$ and…

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 $G$ be a classical algebraic group with Lie algebra ${\mathfrak g}$, and let $U({\mathfrak g})$ be its enveloping algebra. Losev's orbit method gives a natural embedding from t…

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 $V\!ir$ be the Virasoro algebra, $V\!ir^*$ its dual, and let pseudo-orbits be the corresponding coadjoint-orbit analogue. Let $\operatorname{U}(V\!ir)$ denote its universal env…

Let $N$ be the group of triangular matrices over a finite field, let $B$ be the corresponding Borel group, and let $F$ be the flag manifold. The $B$-orbits in $F$ are labeled by el…

Let $G_\mathbb{R}$ be a real reductive Lie group, with complexification $G$ and maximal compact subgroup $K$ as in the source. Let $\mathcal{O}_\mathfrak{p}$ be a nilpotent $K$-orb…

Let $G$ be a reductive group of Hermitian type, with maximal compact subgroup $K$ and Cartan decomposition $g=\mathfrak{k}\oplus\mathfrak{p}$. Let $H<G$ be a closed subgroup, let…

Orbit-model homeomorphism conjecture. The bijection

Orbit-model homeomorphism conjecture. The bijection $\Psi:\Delta(K,N)\to\mathcal{A}(K,N)$ is a homeomorphism for all nilpotent Gelfand pairs.

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…

Let $\VV'_\z$ be the $\QQ(v)$-vector space with basis given by the isomorphism classes of objects in $\fQ'_\z$. For each $K$-orbit $X$ on $\cb^\vt$, let $[X]\in\VV'_\z$ be the elem…