Horn's conjecture with positivity of Littlewood-Richardson coefficients = Horn의 추측과 Littlewood-Richardson 계수의 양성

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We discuss the problem given by Hermann Weyl about relations of real sequences $\alpha$, $\beta$ and $\gamma$ that are eigenvalues of $n \times n$ Hermitian matrices $A$, $B$ and $A+B$ respectively. In the conjecture of Alfred Horn, triples $(\alpha, \beta, \gamma)$ form a convex set defined by some inequalities. This corresponds to another conjecture about positivity of Littlewood-Richardson coefficients called the saturation conjecture. After several proofs of the saturation conjecture appeared, the Horn's conjecture turned out to be true. We focus on the duality between hive models and honeycomb models which are main ideas of two distinct proofs of the saturation conjecture.
Advisors
Baek, Sanghoonresearcher백상훈researcher
Description
한국과학기술원 :수리과학과,
Publisher
한국과학기술원
Issue Date
2020
Identifier
325007
Language
eng
Description

학위논문(석사) - 한국과학기술원 : 수리과학과, 2020.8,[ii, 57 p. :]

Keywords

Littlewood-Richardson coefficients▼aHorn's conjecture▼asaturation conjecture▼ahive models▼ahoneycomb models; Littlewood-Richardson 계수▼aHorn의 추측▼a포화 추측▼ahive 모형▼ahoneycomb 모형

URI
http://hdl.handle.net/10203/284971
Link
http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=925131&flag=dissertation
Appears in Collection
MA-Theses_Master(석사논문)
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