Involutions on pro-$p$-Iwahori Hecke algebras

Abstract

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 module. We calculate ${\pi }^{\iota }$ for simple modules $\pi$. We also calculate the dual of $\pi$.

arXiv comment29 pages. arXiv admin note: text overlap with arXiv:1612.01312

References in corpus (1)

• On pro-$p$-Iwahori invariants of $R$-representations of reductive $p$-adic groups

Cited by in corpus (1)

• Representations of a $p$-adic group in characteristic $p$