2 problems

Let $\mu \in \mathbb{N}^{\ell}$, and let $\ell(\mu):=\lvert\{i=1,\dotsc,\ell:\mu_i>0\}\rvert$ be the number of nonzero entries of $\mu$. For the $\widehat{\mathfrak{sl}}_n$-crystal…

Let $\mathbb{Z}_r\wr S_n$ be the wreath product, and let absolute involutions be mapped to shapes by the colored RSK. For each fixed number of cycles, consider the submodule spanne…