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arXiv · 1908.08502

A Pieri rule for Demazure characters of the general linear group

Sami Assaf·Danjoseph Quijada
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Abstract

The Pieri rule is a nonnegative, multiplicity-free formula for the Schur function expansion of the product of an arbitrary Schur function with a single row Schur function. Key polynomials are characters of Demazure modules for the general linear group that generalize the Schur function basis of symmetric functions to a basis of the full polynomial ring. We prove a nonsymmetric generalization of the Pieri rule by giving a cancellation-free, multiplicity-free formula for the key polynomial expansion of the product of an arbitrary key polynomial with a single part key polynomial. Our proof is combinatorial, generalizing the Robinson--Schensted--Knuth insertion algorithm on tableaux to an insertion algorithm on Kohnert diagrams.

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Sami Assaf, Danjoseph Quijada. 2019-08-22. A Pieri rule for Demazure characters of the general linear group. https://arxiv.org/abs/1908.08502

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