13 problems

Height-three induction conjecture.

Restriction branching conjecture. Except for $A$, the only $\lambda^A$-normal node of residue $\alpha$ is $B$, and

Induction branching conjecture. There are exactly two such conormal nodes, and

Parabolic branching polynomial positivity conjecture. The polynomial $b_{\nu,\overline{\lambda}+\gamma}(p)$ has nonnegative integer coefficients at least when…

Let $k\in\mathbb{N}$ and let $\lambda\vdash 2^k$. Write $l(\lambda)$ for the number of parts of $\lambda$, let $\lambda_{l(\lambda)}$ be its smallest part, and let $Z^\lambda$ be t…

Let $s=(s_1,\ldots,s_n)$, let $\theta=\{\theta_{ij}\}_{1\leqslant i<j\leqslant n}$ be nonnegative integers, and define … The branching coefficients $e_n(s;\theta;q,t)$ are defined…

The $(\mathrm{C}_n,\mathrm{B}_n)$ branching-rule conjecture. The two displayed identities hold.

The branching coefficient formula. The coefficients are

Let $\sigma$ be an involution of ${\mathfrak g}$, let $H_1,\ldots,H_l$ be the chosen basic invariants with degrees $d_1,\ldots,d_l$, and let $\varpi$ be the symmetrisation map. Let…

Let $n\geq 2$ and let $\Gamma$ be a subgroup of $\mathbf{SL}_n\mathbb{C}$. Let $\{\gamma_0,\ldots,\gamma_l\}$ be the equivalence classes of irreducible finite-dimensional complex r…

Associated-variety equality conjecture. The inclusion in that theorem is equality:

Discrete decomposability equivalence conjecture. The following two conditions on $(G,G',\pi)$ are equivalent: (i) the restriction $\pi|_{G'}$ is infinitesimally discretely decompos…

Virtually symmetric-type bounded multiplicity conjecture. If $\mathfrak{q}$ is of virtually symmetric type, then the restriction