  We give an explicit computation of the ring structure in wrapped Floer
homology of a class of real Lagrangians in $A_k$-type Milnor fibers. In the
$A_k$-type plumbing description, those Lagrangians correspond to the cotangent
fibers or the diagonal Lagrangians. The main ingredient of the computation is
to apply a version of the Seidel representation. For a technical reason, we
first carry out computations in v-shaped wrapped Floer homology, and this in
turn gives the desired ring structure via the Viterbo transfer map.
