Extension between simple modules of pro-$p$-Iwahori Hecke algebras

TL;DR

This paper computes the extension groups between simple modules of pro-$p$-Iwahori Hecke algebras, providing insights into their module category structure.

Contribution

It offers the first explicit calculation of extension groups between simple modules in this algebraic setting.

Findings

Extension groups are explicitly calculated for simple modules.

Results reveal the structure of the module category.

New methods for computing extensions are introduced.

Abstract

We calculate the extension groups between simple modules of pro-$p$-Iwahori Hecke algebras.