3 problems

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…

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…