3 problems

Fix $w\in{}^MW$, and let $\nu:T^c(\mathbb{Z}_p)\to\mathbb{C}_p^\times$ be a continuous character. For a character $\lambda$ of $T^+$ or $T^-$, let $v(\lambda)$ denote its slope in…

Let $w\in{}^MW$, $\kappa\in X^\star(T^c)^{M_\mu,+}$, and let $\chi:T(\mathbb{Z}_p)\to {\overline{F}}^\times$ be a finite-order character. For a character $\lambda$ of $T^+$ or…

Let $\be X^\star(T^c)^{M_\mu,+}$ and let $:T(\mathbb{Z}_p)\to\overline{F}^{\times}$ be a finite-order character. For $w\in C^+$, set $=-w^{-1}w_{0,M}(+)-$. Let…