The $N-\Delta$ Weak Axial-Vector Amplitude $C_{5}^a(0)$

The weak $N-\Delta$ axial-vector transition amplitude $<\Delta| A_{\pi ^{+}}^\mu |N>$ - important in $N^{*}$ production processes in general and in isobar models describing $\nu_\mu N\to \mu \Delta$ processes in particular - is examined using a broken symmetry algebraic approach to QCD which involves the realization of chiral current algebras. We calculate a value for the form factor $C_{5}^{A}(0)$ in good agreement with experiment.