On the structures of hive algebras and tensor product algebras for general linear groups of low rank

DOI10.1142/S0218196719500462zbMath1472.20099arXiv1712.02454OpenAlexW2945524012MaRDI QIDQ5242788

Donggyun Kim, Euisung Park, Sangjib Kim

Publication date: 7 November 2019

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.02454

zbMATH Keywords

hivegeneral linear groupLittlewood-Richardson coefficientshighest weight vectorHilbert-Poincaré seriestensor product decompositiontensor product algebra

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Representation theory for linear algebraic groups (20G05) Actions of groups on commutative rings; invariant theory (13A50) Combinatorial aspects of groups and algebras (05E16)

Uses Software

• Macaulay2
• Normaliz

Cites Work

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• An \(S_3\)-symmetric Littlewood-Richardson rule
• Toric degeneration of branching algebras
• Puzzles, tableaux, and mosaics
• The saturation conjecture (after A. Knutson and T. Tao). With an appendix by William Fulton
• A positive proof of the Littlewood-Richardson rule using the octahedron recurrence
• Pieri and Littlewood-Richardson rules for two rows and cluster algebra structure
• A presentation of the double Pieri algebra
• A basis for the \(\mathrm{GL}_n\) tensor product algebra
• The hive model and the polynomial nature of stretched Littlewood-Richardson coefficients
• The Littlewood-Richardson rule and Gelfand-Tsetlin patterns
• The honeycomb model of $GL_n(\mathbb C)$ tensor products I: Proof of the saturation conjecture
• Why should the Littlewood–Richardson Rule be true?

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