10 problems

Let $F$ be a non-archimedean local field. Let $\pi_1$ and $\pi_2$ be Arthur type representations of $\operatorname{GL}_n(F)$ and $\operatorname{GL}_{n-1}(F)$, respectively. Say tha…

Projectivity conjecture. The restriction $\pi|_H$ is projective if and only if $\pi$ is supercuspidal.

Let $pi in \mathrm{Irr}(G_{n+1})$ and $pi' in \mathrm{Irr}(G_n)$. A pair $(pi,pi')$ is relevant if there exist multisegments $\mathfrak m,\mathfrak n$ such that…

Let $G$ be a real almost algebraic group, let $\pi$ be a discrete series representation attached to a coadjoint orbit $\mathcal{O}_{\pi}$, and let $H$ be a closed almost algebraic…

Let $G_n=\mathrm{GL}_n(F)$, and let $\pi_M$ and $\pi_N$ be Arthur type representations of $G_{n+1}$ and $G_n$, respectively. For $k\geq 1$, write $\pi_M^{[k]}$ and…

Let $\mathfrak m$ be a multisegment for $n+1$, and let $\zeta(\mathfrak m)$ denote the associated Zelevinsky induced module. For the restriction to $G_n$, a Bernstein component is…

Let $G$ be a real reductive group, let $G'$ be a reductive subgroup, and choose a maximal compact subgroup $K$ of $G$ such that $K'=G'\cap K$ is a maximal compact subgroup of $G'$.…

Januszewski's conjecture. In the setting of Kobayashi's conjecture, $m_{\tau}(\pi|_{G'})$ grows at most polynomially in the norm of the infinitesimal character of $\tau$, in the se…

Kobayashi's conjecture. The multiplicity $m_{\tau}(\pi|_{G'})$ is finite for every $\tau\in\hat{G}'$. This is a finite-multiplicity assertion for discretely decomposable restrictio…

Interlacing-pattern conjecture. There exists a bijective correspondence between $I(a_.,b_.)$ and discrete series representations $(\pi_1,\pi_2)$ of relevant pairs $(G,H)$ with thes…