  In this article, we study the modular representations of the special linear
group of degree two over a finite field in defining characteristic. In
particular, we study the automorphisms of derived category of representations.
We have been able to obtain a new type of autoequivalence. This autoequivalence
has some uncommon features. It is more conveniently conceived and proved using
the representation theory of its Brauer correspondence but at the same time it
can be very neatly described, using a type of derived equivalence called
perverse equivalence, in global settings.
