Multiplicities of some maximal dominant weights of the \(\widehat{s\ell }(n)\)-modules \(V (k \Lambda_0)\)

DOI10.1007/S10468-021-10031-3OpenAlexW3131876536MaRDI QIDQ2118271

Rebecca L. Jayne, Kailash C. Misra

Publication date: 22 March 2022

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

Full work available at URL: https://arxiv.org/abs/2004.14470

zbMATH Keywords

Young tableaucrystal baseaffine Lie algebralattice pathpattern-avoiding permutation

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Permutations, words, matrices (05A05) Combinatorial aspects of representation theory (05E10) Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67)

Cites Work

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• On multiplicities of maximal weights of \(\widehat{sl}(n)\)-modules
• Combinatorics of representations of \(U_ q (\widehat{\mathfrak sl}(n))\) at \(q=0\)
• Lattice paths, Young tableaux, and weight multiplicities
• Longest Increasing and Decreasing Subsequences
• Pattern avoidance seen in multiplicities of maximal weights of affine Lie algebra representations
• The Hook Graphs of the Symmetric Group

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