4 problems

Let $\Lambda_n$ be the indexing set of weights, let $W$ be the relevant Weyl group, and let $\mathcal{A}^w$ denote the orbit or alcove associated with $w\in W$. For…

Let $P_1^l(n)$ be the set of $l$-tuples of non-negative integers summing to $n$, and let $P(\boldsymbol{\lambda})$ denote the orbit of $\boldsymbol{\lambda}$. For a regular…

Let $P_1^l(n)$ be the set of $l$-tuples of non-negative integers summing to $n$. Let $\boldsymbol{\lambda},\boldsymbol{\mu}\in P_1^l(n)$ be regular, with $\boldsymbol{\mu}$ in the…

Let $p$ be a prime, let $l\geq 2$, and fix the data $(e,l,n,\kappa)$ of a generalized blob algebra. For a regular $\boldsymbol{\lambda}\in P_1^l(n)$, let…