3 problems

Lehrer–Zhang's kernel threshold conjecture. The kernel is nonzero if and only if $r\geq r_c$:

Let $m,n$ be natural numbers and fix a block ${\mathcal B}$ of atypicality $k$ in ${\mathcal F}(\operatorname{SOSP}(m|2n))$. Let $\mathbb{H}_k^\infty$ be the limiting graded diagra…

Let ${\mathcal F}(\operatorname{SOSP}(m|2n))$ be the category of finite-dimensional representations of the orthosymplectic Lie supergroup, let ${\mathcal B}$ be a block of atypical…