8 problems

GLS criterion. For a multisegment $\mathfrak{m}$, $Z(\mathfrak{m})$ is square-irreducible if and only if the GLS condition is satisfied.

Let $\Pi$ be a cuspidal support, let $\mathcal{O}(\Pi)$ denote the corresponding Zelevinsky line, and let $\mathbf{a}$ and $\mathbf{b}$ be multisegments belonging to the same…

Unique embedding conjecture. The embedding

Normalized intertwining-cokernel conjecture. One has

Zelevinsky pole conjecture. One has

Ladder generalization conjecture. The same equivalences remain true when $[a,a]$ is replaced by any ladder ${\bf m}$.

Let $\rho$ be a fixed cuspidal representation, let $d4c$ be an irreducible representation in $d4c\mathrm{rr}_{\rho}$, and let $\mathfrak n\in\mathrm{Mult}_{\rho}$ be minimal to…

Deficiency-length conjecture. The GLS condition, equivalently $d=0$, is equivalent to $l=1$. Moreover, $d=1$ if and only if $l=2$, and this condition is equivalent to…