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Generalized Littlewood-Richardson coefficients for branching rules of GL(N) and extremal weight crystals

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Author(s): Brett Collins
Series: PhD thesis at University of Missouri
Year: 2018

Language: English

Acknowledgements
Abstract
Introduction
Background and motivation
Horn's conjecture
Stretched polynomials and Geometric Complexity Theory
Branching rules
Main results
Organization of the thesis
Background material
Representation theory of `39`42`"613A``45`47`"603AGL(n)
Schur modules
The complexity of Littlewood-Richardson coefficients
Quiver theory
Preliminaries
Semi-invariants for quivers
-semi-stability
The facets of the cone of effective weights
Matrix equations and moment maps
A quiver interpretation of generalized Littlewood-Richardson coefficients
Saturation properties
Sun quiver
Generalized star quiver
The facets of the cones of effective weights
Horn-type inequalities
Sun quiver
Generalized star quiver
Generalized eigenvalue problems
Generalized eigenvalue problem for f1
Generalized eigenvalue problem for f2
The combinatorics and complexity of generalized Littlewood-Richardson coefficients
Factorization formulas
Level-1 weights and stretched polynomials
Level-1 weights
Stretched weights
Polytopal description and complexity
Polytopal description
Appendix
Index of symbols
Index
Bibliography
Vita