On Decomposition of the Product of Demazure atoms and Demazure Characters
Degree type
Graduate group
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Demazure atoms
Demazure characters
key polynomials
skyline fillings
SSAF
Mathematics
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Abstract
This thesis 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.