Algebraic Graph Theory Seminar - Nathan Lindzey

Monday, October 3, 2022 11:30 am - 11:30 am EDT (GMT -04:00)

Title: Jack Derangements

Speaker: Nathan Lindzey
Affiliation: Technion
Location: Contact  Sabrina Lato for Zoom link

Abstract: For each integer partition $\lambda \vdash n$ we give a simple combinatorial formula for the sum of the Jack character $\theta^\lambda_\alpha$ over the integer partitions of $n$ with no singleton parts. For $\alpha = 1,2$ this gives closed forms for the eigenvalues of the permutation and perfect matching derangement graphs, resolving an open question in algebraic graph theory. Our proofs center around a Jack analogue of a hook product related to Cayley's $\Omega$--process in classical invariant theory, which we call \emph{the principal lower hook product}.