Journal of Combinatorics

Volume 3 (2012)

Number 3

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

Pages: 563 – 589

DOI: http://dx.doi.org/10.4310/JOC.2012.v3.n3.a9

Authors

Chris Berg (Fields Institute, York University, and LACIM at UQAM)

Nantel Bergeron (Fields Institute and York University)

Hugh Thomas (University of New Brunswick)

Mike Zabrocki (Fields Institute and York University)

Abstract

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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