3 problems

Let $\boldsymbol{\alpha}=(\alpha_1,\ldots,\alpha_m)$ and $\boldsymbol{\beta}=(\beta_1,\ldots,\beta_m)$ be parameter tuples, and let $\left|G;\Lambda,\boldsymbol{\alpha}\right>$ and…

Let $\mathbf{u}=(u_1,\ldots,u_m)$ and $\mathbf{v}=(v_1,\ldots,v_m)$, and let $\Phi(w)=\Phi_{\mathbf{u}}^{\mathbf{v}}(w):\mathcal{F}_{\mathbf{u}}\to\mathcal{F}_{\mathbf{v}}$ be the…

Let $m$ be a positive integer, let ${\boldsymbol \lambda}=(\lambda^{(1)},\ldots,\lambda^{(m)})$ be an $m$-tuple of partitions, and let $\mathcal{F}_{\mathbf{u}}$ and…