Meeting Details

Title: Combinatorics and Representation Theory of Generalized Permutohedra Student Geometric Functional Analysis Seminar Nicholas Early, Penn State The usual approach to the homology of simplicial complexes of simple Lie type starts from the symmetry and incidence relations of root hyperplanes $x_i=x_j$. We shall sketch what we need from a new framework, due to Adrian Ocneanu, in which generalized permutohedral cones, called plates, subject to homological relations, are now the fundamental building blocks. The symmetric group, which acts by permuting coordinates, decomposes the linear space of plates into irreducible representations. We shall discuss some ideas which led us to a proof of a conjecture of Ocneanu for the character of the action of the symmetric group on the module of plates in a simplex.