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arXiv · 1606.02291

On Deposition of the Product of Demazure Atoms and Demazure Characters

Anna Ying Pun
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Abstract

This paper studies the properties of Demazure atoms and characters using linear operators and also tableaux-combinatorics. It proves the atom-positivity property of the product of a dominating monomial and an atom, which was an open problem. Furthermore, it provides a combinatorial proof to the key-positivity property of the product of a dominating monomial and a key using skyline fillings, an algebraic proof to the key-positivity property of the product of a Schur function and a key using linear operator and verifies the first open case for the conjecture of key-positivity of the product of two keys using linear operators and polytopes.

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Anna Ying Pun. 2016-06-07. On Deposition of the Product of Demazure Atoms and Demazure Characters. https://arxiv.org/abs/1606.02291

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