On irreps of a Hecke algebra of a non-reductive group

David Kazhdan, Alexander Yom Din

We study irreducible representations of the Hecke algebra of the pair $({\mathrm{PGL}}_2(F[\epsilon ]/({\epsilon }^2)),{\mathrm{PGL}}_2(\mathcal{O}[\epsilon ]/({\epsilon }^2)))$ where $F$ is a local non-Archimedean fie…