15 problems

Let $\mathfrak h_{g,1}^{\mathbb Q}$ be the graded Lie algebra under consideration, and let $\operatorname{Sp}$ act on it through the symplectic action on $H_{\mathbb Q}$. Define…

Let $X=G/H$ be an affine homogeneous spherical variety with abelian regular centralizers and no type $N$ roots. Let $S_X$ be the corresponding symplectic representation of…

Let $X=G/H$ be an affine homogeneous spherical variety with abelian regular centralizers, let $G_X^\vee\subset G^\vee$ be its dual group, and let $V_X$ be the representation occurr…

Let $\mu_{n,k}^{\mathrm{Sp}}$ be the symplectic measure defined by the paper, with specializations … Let the associated symplectic Young diagram be sampled using the Berele samplin…

Let $\lambda$ range over partitions, let $h^{\lambda}(u)$ denote the hook length of a cell $u\in\lambda$, and let $c_{sp}^{\lambda}(u)$ be its symplectic content. For an indetermin…

Dual Coulomb-branch conjecture. One has

Hu's generalized surjectivity conjecture. The natural map $\psi'_{f,K}$ is surjective. The paper states that this conjecture implies the preceding algebraically closed-field conjec…

Hu's surjectivity conjecture. The map $\psi_{f,K}$ is surjective. This conjecture asks for the symplectic double-centralizer property on the quotient by the $f$-th Brauer ideal; it…

For partitions $\lambda,\mu,\nu$ of length at most $m$, let $\chi_\lambda$ be the irreducible character of $Sp(2m)$ indexed by $\lambda$, and let…

Let $V(\lambda)$ and $V(\nu)$ be irreducible representations of $Sp(2m)$ indexed by partitions, and let $L(\mu)$ be the irreducible representation of $GL(2m)$ indexed by a partitio…

Let $\mathfrak{sp}_{2n}$ be the symplectic Lie algebra, let $V_{\nu}$ be its standard representation, let $V_{\mathbf{0}}$ be its trivial representation, and let $V_{\lambda}$ be t…

Let $H$ be the symplectic representation underlying the Johnson cokernel, let $D_{2s}$ be the dihedral group of order $2s$, and write $[H^{\langle s\rangle}]_{D_{2s}}$ for the corr…

Let $({\mathfrak m},V,\omega)$ be a symplectic representation of the Lie algebra ${\mathfrak m}$. A subspace $W\subseteq V$ is coisotropic when $W^{\perp_\omega}\subseteq W$, where…

Composition-factor conjecture. The vectors $v_{k,0}$ and $z_{k,0}$ are non-zero in $B_3(A'_{2n})$, and the $H_{2n}$-module composition factors of $B_3(A'_{2n})$ are

Let $f$ be an integer with $1\leq f\leq [n/2]$, let $K$ be an infinite field, let $V$ be the natural symplectic $K$-vector space, and let $\mathfrak{B}_n^{(f)}$ denote the relevant…