  All finite dimensional irreducible representations of the simple Lie-Kac
super algebra SU(2/1) are explicitly constructed in the Chevalley basis as
complex matrices. For typical representations, the distinguished Dynkin label
is not quantized. We then construct the generic atypical indecomposable quivers
classified by Marcu, Su and Germoni and typical indecomposable N-generations
block triangular extensions for any irreducible module and any integer N. In
addition to the quadratic and cubic super-Casimir operators $C_2$ and $C_3$,
the supercenter of the enveloping algebra contains a chiral ghost super-Casimir
operator T of mixed order (2,4)in the odd generators, proportional to the
superidentity grading operator $\chi$, and satisfying $T = \chi\;C_2$ and we
define a new factorizable chiral-Casimir $T^-=C_2(1-\chi)/2=(UV+WX)(VU+XW)$
where (U,V,W,X) are the odd generators. In most indecomposable cases, the
super-Casimirs are non diagonal. We compute their pseudo-eigenvalues.
