A study of the representations supported by the orbit closure of the determinant

DOI10.1112/S0010437X14007660zbMath1328.14077arXiv1109.5996MaRDI QIDQ4982978

Shrawan Kumar

Publication date: 13 April 2015

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1109.5996

zbMATH Keywords

Latin squaresrepresentationsgeometric complexity theoryAlon-Tarsi conjectureValiant's conjecturedeterminant orbit closure

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Representation theory for linear algebraic groups (20G05) Geometric invariant theory (14L24) Group actions on varieties or schemes (quotients) (14L30) Classical groups (algebro-geometric aspects) (14L35)

Related Items (13)

Equations for GL invariant families of polynomials ⋮ Rectangular Kronecker coefficients and plethysms in geometric complexity theory ⋮ Vanishing symmetric Kronecker coefficients ⋮ Algebraic geometry and representation theory in the study of matrix multiplication complexity and other problems in theoretical computer science ⋮ Permanent versus determinant: Not via saturations ⋮ On vanishing of Kronecker coefficients ⋮ Stability of the Levi-Civita tensors and an Alon-Tarsi type theorem ⋮ Symmetrizing tableaux and the 5th case of the Foulkes conjecture ⋮ Fundamental invariants of orbit closures ⋮ No occurrence obstructions in geometric complexity theory ⋮ The Alon-Tarsi conjecture: a perspective on the main results ⋮ Connections between conjectures of Alon-Tarsi, Hadamard-Howe, and integrals over the special unitary group ⋮ Geometric complexity theory: an introduction for geometers

Cites Work

• Geometry of orbits of permanents and determinants
• Nonvanishing of Kronecker coefficients for rectangular shapes.
• \((\mathrm{GL}_n,\mathrm{GL}_m)\)-duality and symmetric plethysm
• Colorings and orientations of graphs
• On Macdonald's \(\eta\)-function formula, the Laplacian and generalized exponents
• On the relations of various conjectures on Latin squares and straightening coefficients
• On the number of even and odd Latin squares of order \(p+1\)
• Geometric Complexity Theory I: An Approach to thePvs.NPand Related Problems
• An Overview of Mathematical Issues Arising in the Geometric Complexity Theory Approach to $\mathbf{VP}\neq\mathbf{VNP}$
• Symmetry, Representations, and Invariants
• Geometric Complexity Theory II: Towards Explicit Obstructions for Embeddings among Class Varieties
• The Conjectures of Alon–Tarsi and Rota in Dimension Prime Minus One

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