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{\bf A. M. Garsia and A. Goupil}
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{\bf Character Polynomials, their q-Analogs and the Kronecker Product }
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The numerical calculation of character values as well as Kronecker
coefficients can efficently be carried out by means of character
polynomials. Yet these polynomials do not seem to have been given a
proper role in present day literature or software. To show their
remarkable simplicity we give here an ``{umbral}'' version and a
recursive combinatorial construction.  We also show that these
polynomials have a natural counterpart in the standard Hecke algebra
${\cal H}_n(q\, )$.  Their relation to Kronecker products is brought to the
fore, as well as special cases and applications.  This paper may also
be used as a tutorial for working with character polynomials in the
computation of Kronecker coefficients.


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