Involutions on pro-$p$-Iwahori Hecke algebras

Noriyuki Abe

The pro-$p$-Iwahori Hecke algebra has an involution $\iota$ defined in terms of Iwahori-Matsumoto basis. Then for a module $\pi$ of pro-$p$-Iwahori Hecke, ${\pi }^{\iota }=\pi \circ \iota$ is also a modul…