12 problems

Let $V$ be a vertex operator algebra satisfying the conditions in the earlier conjecture on products of twisted intertwining operators, and let $G$ be a finite group of automorphis…

Zelevinsky pole conjecture. One has

Intertwining-pole conjecture. One has

Duality conjecture. There exists a maximally extended multivalued analytic function $f(z_1,z_2;w_1,w_2,w_3,w_4)$ on

Whittaker-space isomorphism conjecture. For every $W$-orbit $\mathcal{O}\subset\mathscr{X}_{Q,n}$, the embedding is an isomorphism

Let $M^*_{c,a}(s,\tau,\sigma_{\bar{r}})$ be the normalized intertwining operator introduced above, with $s\in\mathbb{C}$. Nonvanishing conjecture. The operator…

Strong nonvanishing conjecture. The operator $M^*(s,\rho_c(\tau_a)\otimes \rho_d(\tau_b))$ is nonzero for every $s\in\mathbb{C}$.

Twisted intertwining-operator conjecture. The twisted intertwining operators among the $g$-twisted $V$-modules, for all $g\in G$, satisfy associativity, commutativity and modular i…

Intertwining-operator conjecture. For all $1<l\leq r$, $M(\zeta,w_{(k^{l})})$ is well defined at $\zeta=\zeta^{(l)}$ and has irreducible image. For all $c\geq1$,…

Let $F$ be the relevant number field, let $\nu$ be a place of $F$, and let $\tau_\nu$ be the local representation used to form the induced representations. For $l\geq 2$, write…

Let $V$) be a simple vertex operator algebra satisfying the following conditions: $V_{(0)}=\mathbb{C}\mathbf{1}$, $V_{(n)}=0$ for $n<0$, and the contragredient $V'$ is equivalent t…

The local intertwining relation conjecture. Given $\phi_M$ and $u$ as above, one expects