Predavateljica: Olga Azenhas – Portugalska

Working with the classical Littlewood-Richardson rule for composing partitions we present an explicit involution on the set of Littlewood-Richardson tableaux which exhibits the well-known commutative property of this rule.
This bijection is defined by means of a projection of Littlewood-Richardson tableaux.
We also explore the relationship of this combinatorial transformation with the generation of some well-known linear inequalities for the eigenvalues of a sum of Hermitian matrices and the invariant factors of a product of integral matrices.