Doubly adapted bases for the symmetric group

02/28/2012 - 12:15pm
02/28/2012 - 1:10pm
Mike Orrison (HMC)

When it comes to applications of the representation theory of finite groups, adapted bases always seem to be lurking in the background. These are bases of group ring modules that respect, in a very straightforward way, the action of nested subgroups of the group in question. Such bases are, for example, a crucial component in most constructions of fast Fourier transforms for abelian and nonabelian groups alike. In this talk, I'll describe an adapted basis for the regular representation of the symmetric group that is "doubly adapted" in that it respects both the left and right action of the symmetric group on itself. I'll then explain why we think such bases might be the key to a new approach for creating fast Fourier transforms for finite groups. This is joint work with Michael Hansen and Masanori Koyama.

Millikan 208 (Pomona College)