Abstract by John Garrett
Schur-Rings and Character Tables
A Schur ring over a group G is a subring of the group algebra QG that is determined by a partition of G.
Given a subgroup H of GL(n,F_2), the orbits of H acting on the vector space (F_2)^n determine a commutative Schur ring over (C_2)^n.
Let CT(H) denote the character table of the Schur ring. We have noticed that for n < 6 any two sets of orbits are automorphically equivalent if and only if
their character tables are permutation equivalent. We aim to prove this in general.