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arXiv · 1203.4729

Raising operators and the Littlewood-Richardson polynomials

Alex Fun
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Abstract

We use Young's raising operators to derive a Pieri rule for the ring generated by the indeterminates $h_{r,s}$ given in Macdonald's 9th Variation of the Schur functions. Under an appropriate specialisation of $h_{r,s}$, we derive the Pieri rule for the ring $\La(a)$ 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.

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Alex Fun. 2012-03-21. Raising operators and the Littlewood-Richardson polynomials. https://arxiv.org/abs/1203.4729

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