On Decomposition of the Product of Demazure atoms and Demazure Characters
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Degree type
Doctor of Philosophy (PhD)
Graduate group
Mathematics
Discipline
Subject
decomposition of products
Demazure atoms
Demazure characters
key polynomials
skyline fillings
SSAF
Mathematics
Demazure atoms
Demazure characters
key polynomials
skyline fillings
SSAF
Mathematics
Funder
Grant number
License
Copyright date
2016-11-29T00:00:00-08:00
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Author
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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.
Advisor
James Haglund
Date of degree
2016-01-01