Raising operators and the Littlewood-Richardson polynomials

Alex Fun

Abstract

We use Young's raising operators to derive a Pieri rule for the ring generated by the indeterminates given in Macdonald's 9th Variation of the Schur functions. Under an appropriate specialisation of these indeterminates, we derive the Pieri rule for the ring of double symmetric functions, which has a basis consisting of the double Schur functions. Together with a suitable interpretation of the Jacobi-Trudi identity, our Pieri rule allows us to obtain a new proof of a rule to calculate the Littlewood-Richardson polynomials, which gives a multiplication rule for the double Schur functions.

AMS Subject Classification: Primary 05E05.