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

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

2011-07-19

arxiv.org/abs/1107.3610v1

Mathematics

Combinatorics

Scientific paper

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

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