Title: The normal distribution is freely selfdecomposable,
Abstract: The class of selfdecomposable distributions in free probability theory was
introduced by Barndorff-Nielsen and the third named author. It constitutes a
fairly large subclass of the freely infinitely divisible distributions, but so
far specific examples have been limited to Wigner's semicircle distributions,
the free stable distributions, two kinds of free gamma distributions and a few
other examples. In this paper, we prove that the (classical) normal
distributions are freely selfdecomposable. More generally it is established
that the Askey-Wimp-Kerov distribution $\mu_c$ is freely selfdecomposable for
any $c$ in $[-1,0]$. The main ingredient in the proof is a general
characterization of the freely selfdecomposable distributions in terms of the
derivative of their free cumulant transform.