Pieri operators on the affine nilCoxeter algebra
Chris Berg, Franco Saliola, Luis Serrano
TL;DR
This paper introduces a new family of operators on the affine nilCoxeter algebra and uses them to prove conjectures related to strong Schur functions, advancing understanding in algebraic combinatorics.
Contribution
It defines and analyzes Pieri operators on the affine nilCoxeter algebra, providing proofs for existing conjectures about strong Schur functions.
Findings
Proved conjectures of Lam, Lapointe, Morse, and Shimozono.
Established properties of Pieri operators in the affine nilCoxeter algebra.
Enhanced understanding of strong Schur functions.
Abstract
We study a family of operators on the affine nilCoxeter algebra. We use these operators to prove conjectures of Lam, Lapointe, Morse, and Shimozono regarding strong Schur functions.
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