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.

Affinoids in the Lubin–Tate perfectoid space and simple supercuspidal representations II: wild case

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.

Exterior square gamma factors for cuspidal representations of $$\mathrm {GL}_n$$: simple supercuspidal representations

10.1007/s00208-020-02106-1

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.

Affinoids in the Lubin–Tate perfectoid space and simple supercuspidal representations II: wild case

10.1007/s11139-021-00476-x

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.

Exterior square gamma factors for cuspidal representations of $$\mathrm {GL}_n$$: simple supercuspidal representations

10.1007/978-981-13-6628-4_4

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

The Character of a Simple Supercuspidal Representation of SL(2, F)