On decomposition of the product of Demazure atoms and Demazure characters / Anna Ying Pun.

Format:

Book

Manuscript

Thesis/Dissertation

Author/Creator:

Pun, Anna Ying, author.

Contributor:

Haglund, James, degree supervisor, degree committee member.

Block, Johnathan, degree committee member.

Panova, Greta, degree committee member.

University of Pennsylvania. Department of Mathematics, degree granting institution.

Language:

English

Subjects (All):

Penn dissertations--Mathematics.

Mathematics--Penn dissertations.

Local Subjects:

Penn dissertations--Mathematics.

Mathematics--Penn dissertations.

Physical Description:

v, 120 leaves : illustrations (some color) ; 29 cm

Production:

[Philadelphia, Pennsylvania] : University of Pennsylvania, 2016.

Summary:

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.

Notes:

Ph. D. University of Pennsylvania 2016.

Department: Mathematics.

Supervisor: James Haglund.

Includes bibliographical references.

OCLC:

961021917