Comparing products of Schur functions and quasisymmetric functions
Name
166325714-MIT.pdf
Description
Full printable version
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3.63 MB
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Checksum (MD5)
42f375896e39b88d91a7d3bf79dee7b1
Author(s)
Pylyavskyy, Pavlo
Advisor(s)
Richard Stanley.
Date Issued
2007
Publisher
Massachusetts Institute of Technology
Abstract
In this thesis a conjecture of Okounkov, a conjecture of Fomin-Fulton-Li-Poon, and a special case of Lascoux-Leclerc-Thibon's conjecture on Schur positivity of certain differences of products of Schur functions are proved. In the first part of the work a combinatorial method is developed that allows to prove weaker versions of those conjectures. In the second part a recent result of Rhoades and Skandera is used to provide a proof of actual Schur positivity results. Several further generalizations are stated and proved. In particular, an intriguing log-concavity property of Schur functions is observed. In addition, a stronger conjecture is stated in language of alcoved polytops. A weaker version of this conjecture is proved using a characterization of Klyachko cone and the theory of Temperley-Lieb immanants.
Description
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2007.
Includes bibliographical references (p. 71-74).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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