Let $k$ be a local field of residue characteristic $p$, and let D be a central
division algebra over $k$ of index $n>2$. How to determine the irreducible complex representations of the group $SL\_1(D)$?
Suggest some reference regarding this.



Representations of $SL_1(D),$ where $D$ a division algebra over a local field
An article by Shai Shechter recently appeared on Math ArXiv:


"Characters of the Norm-One Units of Local Division Algebras of Prime Degree"


<https://arxiv.org/abs/1512.02448>


