On Decomposition of the Product of Demazure atoms and Demazure Characters

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.

Author dc:creator

• Pun, Ying Anna

Advisor dc:contributor.advisor

• James Haglund

Statement dc:rights

• Ying Anna Pun

Language dc:language

en

Repository record dc:identifier.uri

https://repository.upenn.edu/handle/20.500.14332/28824

OAI identifier oai:identifier

oai:repository.upenn.edu:20.500.14332/28824