11 problems

Let $G={\rm SO}(2,1)^\circ$, let $K\cong {\rm SO}(2)$ be a maximal compact subgroup, and let $\Gamma$ be a uniform torsion-free lattice in $G$. Consider the right regular represent…

Let $G/H$ be a reductive homogeneous space in Setting, and let $\operatorname{Disc}(G/H)$ denote its discrete series representations. Kobayashi's conjecture. One has the equivalenc…

Let $G$ be a group such that $G(\mathbb{R})$ admits discrete series, let $\pi^S$ be an automorphic representation that is not $G$-Eisenstein, and write an automorphic cuspidal repr…

Let ${\underline{G}}$ be a connected reductive group defined over $\mathbb{R}$, let $G={\underline{G}}(\mathbb{R})$, and let ${\underline{H}}\subset{\underline{G}}$ be an algebraic…

Let $G=\operatorname{Sp}(2n,\mathbb{R})$. For $0\leq m\leq n-1$, let $\operatorname{Sp}(2m,\mathbb{R})\times \operatorname{Sp}(2n-2m,\mathbb{Z})$ be the subgroup acting on the corr…

Let $G$ be a reductive group with maximal compact subgroup $K=K_1\times K_2$, let $H$ be a subgroup with associated symmetric-pair data $H_0$ and $L$, and let $\pi_\lambda^G$ be an…

Let $({\mathfrak {g}}',K')$ be a reductive pair, let ${\mathfrak {u}}'$ be the nilradical of a parabolic subalgebra, and set $\lambda_0=\rho({\mathfrak {u}}')$. Regularity conjectu…

Conjecture. The representation $\pi$ is holomorphic or anti-holomorphic if and only if $\operatorname{p}_1(\mathcal{O}_{\pi})$ is an open coadjoint $A_1N_1$-orbit in…

Duflo's conjecture. [The supplied candidate statement ends immediately after “Alors:”; no mathematical assertion is present in the input.]

Let $\pi$ be a discrete series representation, and suppose the Blattner formula is obtained from Schmid's upper bound on its $K$-types together with the character formula on a fund…

Let $G$ be the reductive group under consideration, let $\pi$ be a regular discrete series representation of $G(\mathbb{R})$, and let $e_{\pi}$ denote the stable cuspidal test func…