Diamond diagrams and multivariable $(\ddot{I}†,{\mathcal{O}}_K^{\times })$-modules

Yitong Wang

Let $p$ be a prime number and $K$ a finite unramified extension of ${\mathbb{Q}}_p$. Let $\ddot{I}€$ be an admissible smooth mod $p$ representation of ${\mathrm{GL}}_2(K)$ occurring in some H…