Geometry Seminar

Date: September 7, 2015

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Christian Ikenmeyer, Texas A&M University

Title: Plethysms and Kronecker coefficients

Abstract: This talk is a report on the following 3 results. The famous Foulkes conjecture (1950) is a conjecture about the inequality of plethysm coefficients in Sym^a Sym^b V and Sym^b Sym^a V. The conjecture is known for a <= 4. We prove the case $a=5$. We prove and generalize Weintraub's conjecture (1990) that states that all even partitions occur in the plethysm Sym^d Sym^n V for n even. Related to the fundamental positivity questions in representation theory is the following question: What is the computational complexity of deciding the positivity of the Kronecker coefficient? We prove that this is NP-hard.