  The Fourier Transform is one of the most important linear transformations
used in science and engineering. Cooley and Tukey's Fast Fourier Transform
(FFT) from 1964 is a method for computing this transformation in time $O(n\log
n)$. From a lower bound perspective, relatively little is known. Ailon shows in
2013 an $\Omega(n\log n)$ bound for computing the normalized Fourier Transform
assuming only unitary operations on pairs of coordinates is allowed. The goal
of this document is to describe a natural open problem that arises from this
work, which is related to group theory, and in particular to representation
theory.
