Tyrrell McAllister (TU Eindhoven): Applications of
polyhedral geometry to computational representation theory
We discuss several families of polyhedra
that arise in the representation theory of semisimple
Lie algebras. In the past 10 years, work by Berenstein
and Zelevinsky and by Knutson and Tao has shown the
fruitfulness of encoding coefficients related to the
decompositions of representations as the number of
lattice points contained in special families of polytopes.
We discuss in particular applications of polytopes to the
computational complexity of Clebsch--Gordan coefficients.
We also mention some conjectures and results motivated by
the polytopal interpretation of these coefficients.