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The Fourier Transform is one of the most important linear transformationsused in science and engineering. Cooley and Tukey's Fast Fourier Transform(FFT) from 1964 is a method for computing this transformation in time $O(n\logn)$. From a lower bound perspective, relatively little is known. Ailon shows in2013 an $\Omega(n\log n)$ bound for computing the normalized Fourier Transformassuming only unitary operations on pairs of coordinates is allowed. The goalof this document is to describe a natural open problem that arises from thiswork, which is related to group theory, and in particular to representationtheory.

Interesting Open Problem Related to Complexity of Computing the Fourier Transform and Group Theory