A combinatorial proof of the reduction formula for Littlewood–Richardson coefficients

To Professor Georgia Benkart with our best wishes on her retirement
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Abstract

There are well-known reduction formulas for the universal Schubert coefficients defined on Grassmannians. These coefficients are also known as the Littlewood–Richardson coefficients in the theory of symmetric functions. We restate the reduction formulas combinatorially and provide a combinatorial proof for them.

Keywords

Reduction formulae
Littlewood–Richardson coefficient
Schubert calculus

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This research was done while the authors were visiting Korea Institute for Advanced Study.

1

The author was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2006-312-C00014).

2

The author is grateful to Professor Arun Ram for his valuable discussions and suggestions.