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

This article describes the linear representation theory of the projective 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 $$PSL(2,q)$$ or $$PSL_2(q)$$.

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