I will report on some recent work on the commutation relations and normal ordering between families of operators on symmetric functions. These operators can be naturally defined by the operations of multiplication, Kronecker product, and their adjoints. As applications we give a new proof of the skew Littlewood-Richardson rule and prove an identity about the Kronecker product with a skew Schur function. Some effort will be made to motivate these results, and to relate them to classical questions on representation theory.
This is join work with Emmanuel Briand, Peter R.W. McNamara, and Rosa Orellana.
