11 problems

Let $V_{\mu_1},\ldots,V_{\mu_\ell}$ be self-conjugate irreducible representations of a rational vertex algebra, and let $\nu_{\mu_i}\in\{1,-1\}$ denote their Frobenius–Schur indica…

Let $B$ be a real, non-principal $2$-block with defect pair $(D,E)$, and let $\Phi$ be its unique projective indecomposable character. Let $\epsilon$ denote the Frobenius–Schur ind…

Let $B$ be a real, nilpotent, non-principal $2$-block of a finite group $G$ with defect pair $(D,E)$. Let $\operatorname{Irr}(D)$ and $\operatorname{Irr}(B)$ denote the sets of ord…

For a nilpotent block, let $p$ be a prime and let $D$ be its defect group. The extended defect group is the local group associated with the block that extends $D$ by an involution…

Bantay's positivity conjecture. For any such category,

Condensation and coset conjecture. Under fairly general conditions, the condensations and cosets of such theories also have $Z_2$ Frobenius–Schur gradings.

Let $G$ be a finite group with $w$ distinct weakly real $2$-principal indecomposable characters $\Phi_1,\dots,\Phi_w$. Strong matching conjecture. Then $G$ has $w$ distinct symplec…

Let $\Phi$ be a weakly real principal indecomposable character of a finite group. Even-indicator conjecture. The Frobenius–Schur indicator $\epsilon(\Phi)$ is even. The examples pr…

Courter's conjecture. The indicators of all simple modules over $D(S_n)$ are nonnegative.

For an inclusion of symmetric groups $\mathbb S_{n-k}\subset \mathbb S_n$ with $n\geq 2k$, consider the double cosets and classify them according to whether their Frobenius–Schur i…

Higher-indicator conjecture. For every finite real reflection group $G$, every irreducible ${\mathcal D}(G)$-module $V$, and every positive integer $m$,