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On extensions of characters of affine pro-$p$ Iwahori--Hecke algebra

Research paper by Santosh Nadimpalli

Indexed on: 08 Mar '17Published on: 08 Mar '17Published in: arXiv - Mathematics - Representation Theory



Abstract

Let $K$ be a non-discrete non-Archimedean local field with residue characteristic $p$. Let $G$ be the group of $K$ rational points of a algebraic connected reductive group defined over $K$. In this article we compute the extensions between characters of affine pro-$p$ Iwahori--Hecke algebra $\mathcal{H}^{\text{aff}}$ over an algebraically closed field $R$ of characteristic $p$. In rank one case we deduce the relation between the blocks and $L$-packets.