  We construct an infinite tower of irreducible calibrated representations of
periplectic Brauer algebras on which the cup-cap generators act by nonzero
matrices. As representations of the symmetric group, these are exterior powers
of the standard representation (i.e. hook representations). Our approach uses
the recently-defined degenerate affine periplectic Brauer algebra, which plays
a role similar to that of the degenerate affine Hecke algebra in representation
theory of the symmetric group. We write formulas for the representing matrices
in the basis of Jucys--Murphy eigenvectors and we completely describe the
spectrum of these representations. The tower formed by these representations
provides a new, non-semisimple categorification of Pascal's triangle. Along the
way, we also prove some basic results about calibrated representations of the
degenerate affine periplectic Brauer algebra.
