Speaker: Sheila Sundaram (Pierrepont School, Westport, CT)
Title: "On conjugacy classes of Sn containing all irreducibles"
Abstract: The action of Sn on itself by conjugation is a permutation representation whose orbits are the conjugacy classes. It is known that this action contains all the irreducible Sn-modules; several proofs of this fact appear in the literature. Here we establish the fact that there are single classes which contain all the irreducibles, and give a simple characterisation of the orbits containing ALL the irreducibles of Sn. The precise result is the following:
If n ≠ 4,8, the conjugacy class indexed by the integer partition λ of n contains all Sn-irreducibles if and only if λ has all parts distinct and odd, and has at least two parts.