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

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