Some representation theory of the group Sl*(2,A) where A=M(2,O/p^2) and * equals transpose

Let A be a ring with involution *. The group Sl_*(2,A), defined by Pantoja and Soto-Andrade, is a noncommutative version of Sl(2,F) where F is a field. In the case of A being artinian, they determined when Sl_*(2,A) admitted a Bruhat presentation, and with Gutiérrez, constructed a representation for Sl_*(2,A) from its generators. In particular, if A=M_n(F) and * is transposition, then Sl_*(2,A) = Sp(2n,F). In this paper, we are interested in the representation theory of G=Sp₄(O/p²) where A=M₂(O/p²) and O is a local ring with prime ideal p. It has a normal, abelian subgroup K, and by Clifford's theorem we can find distinct irreducible representations of G starting with one-dimensional representations of K. The outline of our strategy will be demonstrated in the example of finding irreducible representations of SL₂,(O/p²).