  The irreducible characters of the symmetric group are a symmetric polynomial
in the eigenvalues of a permutation matrix. They can therefore be realized as a
symmetric function that can be evaluated at a set of variables and form a basis
of the symmetric functions. This basis of the symmetric functions is of
non-homogeneous degree and the (outer) product structure coefficients are the
stable Kronecker coefficients.
  We introduce the irreducible character basis by defining it in terms of the
induced trivial characters of the symmetric group which also form a basis of
the symmetric functions. The irreducible character basis is closely related to
character polynomials and we obtain some of the change of basis coefficients by
making this connection explicit. Other change of basis coefficients come from a
representation theoretic connection with the partition algebra, and still
others are derived by developing combinatorial expressions.
  This document is an extended abstract which can be used as a review reference
so that this basis can be implemented in Sage. A more complete version of the
results in this abstract can be found in {\tt arXiv:1605.06672}.
