  The ring of symmetric functions carries the structure of a Hopf algebra. When
computing the coproduct of complete symmetric functions $h_\lambda$ one arrives
at weighted sums over reverse plane partitions (RPP) involving binomial
coefficients. Employing the action of the extended affine symmetric group at
fixed level $n$ we generalise these weighted sums to cylindric RPP and define
cylindric complete symmetric functions. The latter are shown to be
$h$-positive, that is, their expansions coefficients in the basis of complete
symmetric functions are non-negative integers. We state an explicit formula in
terms of tensor multiplicities for irreducible representations of the
generalised symmetric group. Moreover, we relate the cylindric complete
symmetric functions to a 2D topological quantum field theory (TQFT) that is a
generalisation of the celebrated $\mathfrak{\widehat{sl}}_n$-Verlinde algebra
or Wess-Zumino-Witten fusion ring, which plays a prominent role in the context
of vertex operator algebras and algebraic geometry.
