6 problems

Assume that ${\mathfrak{g}}$ is of finite type. Let $W$ be the Weyl group, let $i\in I$, let $a\in\mathbb{C}^*$, and let $\boldsymbol{\psi}_{w(\omega_i^\vee),a}$ be the correspondi…

Let $p$ be a nonnegative integer and let $r$ satisfy $0\leq r\leq p$. Consider fork representations of $\mathfrak{osp}(2m|2n)$ with Dynkin labels $[0,\ldots,0,r,p-r]$, and the corr…

Let $m,n$ be nonnegative integers with $|m-n|$ even. Let $p$ be a nonnegative integer and $r$ an integer with $0\leq r\leq p$. Consider the representation of…

Let $\lambda$ be a partition and let $\ell(\lambda)$ denote its length. For the corresponding $\mathfrak{so}(2k)$ characters, the Schur-function expansions are subject to the condi…

For every even integer $n\geq 0$, let $V_{-2}(\mathfrak{osp}(n+8\mid n))$ be the associated affine vertex superalgebra, and let $V_{-2}(\mathfrak{so}(8))$ be the affine vertex alge…

Affine Langlands character conjecture. The polynomial