Quaternionic Speh representations

Abstract

For a central division algebra $D$, we study a family of representations of ${\mathrm{GL}}_{k,D}$ (both locally and globally), which can be viewed as analogs of the Speh representations. At the non- Archimedean places, we show that these representations support unique models of degenerate type. Globally, we show that these representations support certain non-vanishing Fourier coefficients. We also obtain some partial results regarding unique models at the Archimedean places.