Perforated tableaux: a combinatorial model for crystal graphs in type \(A_{n - 1}\)

DOI10.1007/s10468-022-10135-4arXiv2007.11721MaRDI QIDQ6090809

Glenn D. Appleby, Tamsen Whitehead

Publication date: 20 November 2023

Published in: Algebras and Representation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.11721

zbMATH Keywords

highest weightcrystal basescrystal graphscombinatorial modelLusztig involutionperforated tableauxSchützenberger evacuation map

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10)

Cites Work

• Unnamed Item
• The octahedron recurrence and \(\mathfrak{gl}_n\) crystals
• Double crystals of binary and integral matrices
• On the combinatorics of crystal graphs. I: Lusztig's involution
• Non-symmetric Cauchy kernels for the classical groups
• Kostka polynomials and energy functions in solvable lattice models
• Crystal graphs for representations of the \(q\)-analogue of classical Lie algebras
• Canonical bases for the quantum group of type \(A_r\) and piecewise-linear combinatorics
• Tableau switching: Algorithms and applications
• Crystal Bases
• On the combinatorics of crystal graphs, II. The crystal commutor
• Combinatorial Howe duality of symplectic type
• Duality and bicrystals on infinite binary matrices

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