Linear representation theory of special linear group of degree two over a finite field

This article describes the linear representation theory of the special linear group of degree two over a finite field. The order (size) of the field is $$q$$, and the characteristic prime is $$p$$. $$q$$ is a power of $$p$$. We denote the group as $$SL(2,q)$$ or $$SL_2(q)$$.

See also the linear representation theories of: general linear group of degree two, projective general linear group of degree two, and projective special linear group of degree two.

For linear representation theory in characteristics that divide the order of the group, refer:


 * Modular representation theory of special linear group of degree two over a finite field in its defining characteristic: In characteristic $$p$$, same as the field characteristic.
 * (Modular representation theory in other characteristics that divide $$q - 1$$ or $$q + 1$$ -- link to be added)