Alternating monodromy from an involution

We give a simple geometric  condition on an involution which
implies  that a  corresponding imprimitive  Galois/monodromy
group is alternating. We use this to determine the monodromy
group  of an  unmixed system  of reciprocal  polynomials and
show how  it explains examples from the  applied mathematics
literature with alternating monodromy.   This is joint work
with Timothy Duff and Josef Schicho.