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Expansion of \(k\)-Schur functions for maximal rectangles within the affine nilCoxeter algebra. (English) Zbl 1291.05218

Summary: 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.

MSC:

05E15 Combinatorial aspects of groups and algebras (MSC2010)
05E05 Symmetric functions and generalizations
14N15 Classical problems, Schubert calculus
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