Iwahori-Hecke algebra and unramified local L-functions

TL;DR

This paper uses Iwahori-Hecke algebra theory to compute Hecke actions and derive new expressions for unramified local L-functions of reductive groups over non-archimedean fields.

Contribution

It introduces a novel method to express unramified local L-functions via Hecke algebra actions, enhancing understanding of their structure.

Findings

New explicit formulas for local L-functions

Hecke action computations for unramified principal series

Application of Iwahori-Hecke algebra theory to local L-functions

Abstract

In this paper, we compute the Hecke action of a certain test function on the space of an unramified principal series of a connected reductive group over a non-archimedean local field by using the theory of Iwahori--Hecke algebra. As an application, we obtain a new expression of the local L-functions of unramified representations.