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

LIBRA QA001 2016 .P9841
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Language:
English
Subjects (All):
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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

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