Inverse Satake isomorphism and change of weight

Noriyuki Abe, Florian Herzig, Marie-France Vignéras

Let $G$ be any connected reductive $p$-adic group. Let $K\subset G$ be any special parahoric subgroup and $V,V^{\prime }$ be any two irreducible smooth ${\overline{\mathbb{F}}}_p[K]$-modules.…