Inhalt

•  
   Introduction
•  
   Main Results
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  Outline and Further Results
•  
   Part I: Geometric Complexity Theory
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   Part II: Littlewood-Richardson Coefficients
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   I Geometric Complexity Theory
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  Preliminaries: Geometric Complexity Measures
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   Circuits and Algebraic Complexity Theory
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   Completeness and Reduction
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   Approximating Polynomials
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   Complexity of Bilinear Maps
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   Tensor Rank and Border Rank
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   Summary and Unifying Notation
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  Preliminaries: The Flip via Obstructions
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   Classical Algebraic Geometry
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   Linear Algebraic Groups and Polynomial Obstructions
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   Representation Theoretic Obstructions
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   Coordinate Rings of Orbits
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   Geometric Invariant Theory
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   Peter-Weyl Theorem
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  Preliminaries: Classical Representation Theory
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   Young Tableaux
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   Explicit Highest Weight Vectors
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   Polarization, Restitution, and Projections
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   Schur-Weyl Duality and Highest Weight Vectors
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   Plethysm Coefficients
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   Plethysm Coefficients and Weight Spaces
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   Kronecker Coefficients
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   Littlewood-Richardson Coefficients
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  Coordinate Rings of Orbits
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  Stabilizers
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   Tensors
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   Polynomials
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  Branching Rules
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   Unit Tensor
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   Determinant, Permanent and Matrix Multiplication
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   Inheritance
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   Generic Tensors
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   Stability and Exponent of Regularity
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  Representation Theoretic Results
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   Kernel of the Foulkes-Howe Map
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   Even Partitions in Plethysms
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  Nonvanishing of Symmetric Kronecker Coefficients
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   Moment Polytopes
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   Asymptotic Result
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  Obstruction Designs
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   Set Partitions
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   Obstruction Designs
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   Symmetric Obstruction Designs
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   Reduced Kronecker Coefficients
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  Explicit Obstructions
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  Some Computations
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   Orbit-wise Upper Bounds
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   Regular Determinant Function
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   m x m Matrix Multiplication
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   Vanishing on the Unit Tensor Orbit
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   Evaluation at the Matrix Multiplication Tensor
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  Further Results
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   Orbit-wise Upper Bound Proof
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   2 x 2 Matrix Multiplication
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  Some Negative Results
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   SL-obstructions
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   Cones and Saturated Semigroups
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   II Littlewood-Richardson coefficients
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  Hive Flows
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  Flow Description of LR Coefficients
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   Flows on Digraphs
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   Flows on the Honeycomb Graph G
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   Hives and Hive Flows
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  Properties of Hive Flows
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   The Support of Flows on G
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   The Graph of Capacity Achieving Integral Hive Flows
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  The Residual Digraph
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   Turnpaths and Turncycles
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   Flatspaces
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   The Rerouting Theorem
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  Algorithms
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   A First Max-flow Algorithm
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   A Polynomial Time Decision Algorithm
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   Enumerating Hive Flows
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   The Neighbourhood Generator
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   A First Approach
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   Bypassing the Secure Extension Problem
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  Proofs
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  Proof of the Rerouting Theorem
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   Canonical Turnpaths in Convex Sets
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   Parallelograms
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   Trapezoids, Pentagons, and Hexagons
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   Triangles
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   Proof of the Shortest Turncycle Theorem
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   Special Rhombi
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   Rigid and Critical Rhombi
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   Proof of the Connectedness Theorem
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   Proof of the King-Tollu-Toumazet Conjecture
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   Proof of Proposition 12.4.4
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   Proof of Key Lemma 12.4.5
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   Proof of Lemma 12.4.11
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   Appendix
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  Calculations
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   Obstruction Candidates
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   List of Algorithms
•  
   Bibliography