5 problems

Surface-tension conjecture. The surface tension remains valid when the constant weights $p$ and $q$ are replaced by the position-dependent weights

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…

Assume there is a bijection between generalized oscillating tableaux of length $k$ with $n$ parts, whose final component is $(m,\ldots,m)$ for some $m\in\mathbb{Z}$, and…

Let a generalized oscillating tableau have length $k$ and $n$ parts, with final component $(m,\ldots,m)$ for some $m\in\mathbb{Z}$. Consider $\operatorname{sl}(n)$ webs with $k$ bo…