Expansion of $k$ -Schur functions for maximal $k$ -rectangles within the affine nilCoxeter algebra

preprint2012arXivOpen access

We give several explicit combinatorial formulas for the expansion of k-Schur functions indexed by maximal rectangles in terms of the standard basis of the affine nilCoxeter algebra. Using our result, we also show a commutation relation of k-Schur functions corresponding to rectangles with the generators of the affine nilCoxeter algebra.

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Expansion of $k$ -Schur functions for maximal $k$ -rectangles within the affine nilCoxeter algebra

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Expansion of kkk-Schur functions for maximal kkk-rectangles within the affine nilCoxeter algebra

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Expansion of $k$ -Schur functions for maximal $k$ -rectangles within the affine nilCoxeter algebra