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