On supercuspidal representations of $SL_n(F)$ associated with tamely ramified extensions

TL;DR

This paper constructs explicit irreducible supercuspidal representations of SL_n over non-archimedean local fields and explores their Langlands parameters by verifying a key formula relating to their formal degrees.

Contribution

It provides an explicit construction method for supercuspidal representations associated with tamely ramified extensions and investigates their Langlands correspondence.

Findings

Verification of the Hiraga-Ichino-Ikeda formula for these representations

Explicit description of supercuspidal representations for SL_n(F)

Insights into the Langlands parameters for tamely ramified cases

Abstract

We will give an explicit construction of irreducible suparcuspidal representations of the special linear group over a non-archimedean local field and will speculate its Langlands parameter by means of verifying the Hiraga-Ichino-Ikeda formula of the formal degree of the supercuspidal representations.