5 problems

Let $\underline{\lambda}$ be a $d$-partition, let $\underline{\emptyset}$ denote the empty $d$-partition, and let $f_i^{(a)}$ be the divided-power operator associated with a residu…

Ariki–Koike representation-theory conjecture. These algebras should play a role in the representation theory of reductive groups similar to, but more complicated than, that played…

Let $\bm\lambda,\bm\mu\in\mathcal{P}^r$ lie in a block $B$ of $\mathcal{H}_{r,n}$, with $\bm\mu$ $e$-multiregular. Obtain $\bm\lambda^{+\varnothing}$ and $\bm\mu^{+\varnothing}$ fr…

Let $\mathbf{s}=(s+1,s,\ldots,s)$ be the spetsial multicharge, and let $\lambda$ be a cylindric $l$-partition. Write … and let $m(\lambda)$ be the multipartition selected by the mi…

Let $\mathcal{H}_n$ be an Ariki–Koike algebra of $G(r,1,n)$, and let $\boldsymbol{\lambda}$ and $\boldsymbol{\mu}$ be multipartitions of $n$ with $r$ components. Let…