Why should the Littlewood–Richardson Rule be true?
From MaRDI portal
Publication:5389599
DOI10.1090/S0273-0979-2011-01358-1zbMath1300.20053OpenAlexW2143851795MaRDI QIDQ5389599
Publication date: 22 April 2012
Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0273-0979-2011-01358-1
tensor productsLittlewood-Richardson ruleLittlewood-Richardson tableauxirreducible polynomial representationsYoung diagramsPieri rulerepresentations of general linear groups\((GL_n,GL_m)\)-duality\(GL_n\) tensor product algebra
Combinatorial aspects of representation theory (05E10) Representation theory for linear algebraic groups (20G05)
Related Items
A product formula for certain Littlewood-Richardson coefficients for Jack and Macdonald polynomials, Pieri and Littlewood-Richardson rules for two rows and cluster algebra structure, Standard bases for tensor products of exterior powers, Sign Hibi cones and the anti-row iterated Pieri algebras for the general linear groups, Highest weight vectors in plethysms, Multiplicity-free Representations of Algebraic Groups, Skew Pieri algebras of the general linear group, Contingency tables and the generalized Littlewood–Richardson coefficients, Hibi algebras and representation theory, Spherical analysis on homogeneous vector bundles, On classical groups detected by the triple tensor product and the Littlewood-Richardson semigroup, On the structures of hive algebras and tensor product algebras for general linear groups of low rank, Sums of squares of Littlewood–Richardson coefficients and GL n -harmonic polynomials, Dirac Cohomology and Generalization of Classical Branching Rules
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Triple multiplicities for \(s\ell (r+1)\) and the spectrum of the exterior algebra of the adjoint representation
- Young diagrammatic methods for the restriction of representations of complex classical Lie groups to reductive subgroups of maximal rank
- Standard monomial theory for flag algebras of GL\((n)\)and Sp\((2n)\)
- q-Catalan numbers
- Eigenvalues of sums of Hermitian matrices
- A generalization of the Littlewood-Richardson rule and the Robinson- Schensted-Knuth correspondence
- On Schensted's construction and the multiplication of Schur functions
- Stable bundles, representation theory and Hermitian operators
- Degenerations of flag and Schubert varieties to toric varieties
- A simple proof of the Littlewood-Richardson rule and applications.
- Toric degeneration of Schubert varieties and Gelfand--Tsetlin polytopes
- Signed posets
- On the decomposition of tensor products of the representations of the classical groups: By means of the universal characters
- Paths and root operators in representation theory
- Convexity properties of the moment mapping. III
- Weyl chambers and standard monomial theory for poset lattice cones
- On a problem of Klee concerning convex polytopes
- A basis for the \(\mathrm{GL}_n\) tensor product algebra
- Stable branching rules for classical symmetric pairs
- Products and Plethysms of Characters with Orthogonal, Symplectic and Symmetric Groups
- Very Basic Lie Theory
- Bases for some reciprocity algebras I
- Analysis on foliated spaces and arithmetic geometry
- Kronecker products for compact semisimple Lie groups
- Geometry of G/P-II [The work of De Concini and Procesi and the basic conjectures]
- Branching rules for classical Lie groups using tensor and spinor methods
- The Geometry of Schemes
- The honeycomb model of $GL_n(\mathbb C)$ tensor products I: Proof of the saturation conjecture
- Eigenvalue Inequalities and Schubert Calculus
- The honeycomb model of 𝐺𝐿_{𝑛}(ℂ) tensor products II: Puzzles determine facets of the Littlewood-Richardson cone
- Sagbi bases with applications to blow-up algebras.
- Eigenvalues, invariant factors, highest weights, and Schubert calculus
- Generalized Young Tableaux and the General Linear Group
- Modification Rules and Products of Irreducible Representations of the Unitary, Orthogonal, and Symplectic Groups
- On invariant theory under restricted groups
- A concise proof of the Littlewood-Richardson rule
