Representations of $SL_1(D),$ where $D$ a division algebra over a local field

The representation theory of ${\rm SL}_1 (D)$ was the topics of Göran Kirchner's PhD (defended in 2007, under the supervision of E.-W. Zink, Berlin). To my knowledge it has not been published.

https://www.amazon.de/Zur-Darstellungstheorie-von-SL1-D/dp/3868059970

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