Is this electronic transition symmetry allowed?

Question

a transition from a state ofA1 symmetry to a state of E1 symmetry excited by z-polarised light

in a molecule belonging to the point group C5v.

Answer 1

Actually

on wikipedia

Answer 2

The transition will be allowed only if the direct product of A1 and E1 transforms as z.  The direct product of A1 and E1 is E1, which transforms as x,y.  So no dice.  A1 --> E1 is not allowed with z-polarized light.  Only A1 --> A1 would be allowed with z-polarized light for a C5v molecule