TITLE: Representations of $SL_1(D),$ where $D$ a division algebra over a local field
QUESTION [8 upvotes]: 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.

REPLY [3 votes]: An article by Shai Shechter recently appeared on Math ArXiv:
"Characters of the Norm-One Units of Local Division Algebras of Prime Degree"
http://front.math.ucdavis.edu/1512.02448