PreprintRaising operators and the LittlewoodRichardson polynomialsAlex FunAbstractWe 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 JacobiTrudi identity, our Pieri rule allows us to obtain a new proof of a rule to calculate the LittlewoodRichardson polynomials, which gives a multiplication rule for the double Schur functions. AMS Subject Classification: Primary 05E05.
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