## What is/are Simple Supercuspidal?

Simple Supercuspidal - We construct a family of affinoids in the Lubin–Tate perfectoid space and their formal models such that the middle cohomology of their reductions realizes the local Langlands correspondence and the local Jacquet–Langlands correspondence for the simple supercuspidal representations.^{[1]}We compute the local twisted exterior square gamma factors for simple supercuspidal representations, using which we prove a local converse theorem for simple supercuspidal representations.

^{[2]}In this paper, we compute the character of a simple supercuspidal representation of SL(2, F), when p is arbitrary.

^{[3]}

## simple supercuspidal representation

We construct a family of affinoids in the Lubin–Tate perfectoid space and their formal models such that the middle cohomology of their reductions realizes the local Langlands correspondence and the local Jacquet–Langlands correspondence for the simple supercuspidal representations.^{[1]}We compute the local twisted exterior square gamma factors for simple supercuspidal representations, using which we prove a local converse theorem for simple supercuspidal representations.

^{[2]}In this paper, we compute the character of a simple supercuspidal representation of SL(2, F), when p is arbitrary.

^{[3]}