Algebraic Graph Theory - Yuval Filmus

Title: Orthogonal basis of eigenvectors for the Johnson and Kneser graphs

Abstract: The Johnson and Kneser graphs have the same eigenspaces. How explicitly can we describe these eigenspaces? We describe an explicit orthogonal basis for each eigenspace, which coincides with the Gelfand–Tsetlin basis. We also discuss related work on other graphs, including many open questions.

Joint work with Nathan Lindzey (Technion).