On the combinatorics of crystal graphs, II. The crystal commutor
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Publication:5438452
DOI10.1090/S0002-9939-07-09244-1zbMath1129.05059arXivmath/0611444MaRDI QIDQ5438452
Publication date: 23 January 2008
Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/math/0611444
Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Representation theory for linear algebraic groups (20G05) Semisimple Lie groups and their representations (22E46)
Related Items (6)
Inverse \(K\)-Chevalley formulas for semi-infinite flag manifolds. II: Arbitrary weights in ADE type ⋮ Perforated tableaux: a combinatorial model for crystal graphs in type \(A_{n - 1}\) ⋮ Promotion, evacuation and cactus groups ⋮ Coboundary categories and local rules ⋮ Promotion on oscillating and alternating tableaux and rotation of matchings and permutations ⋮ InverseK-Chevalley formulas for semi-infinite flag manifolds, I: minuscule weights in ADE type
Cites Work
- Combinatorial models for Weyl characters
- On the combinatorics of crystal graphs. I: Lusztig's involution
- A definition of the crystal commutor using Kashiwara's involution
- An analogue of Jeu de taquin for Littelmann's crystal paths
- Crystal graphs for representations of the \(q\)-analogue of classical Lie algebras
- Tensor product multiplicities, canonical and totally positive varieties
- Paths and root operators in representation theory
- Canonical bases for the quantum group of type \(A_r\) and piecewise-linear combinatorics
- The crystal structure on the set of Mirković-Vilonen polytopes
- Crystals and coboundary categories
- Crystalizing the q-analogue of universal enveloping algebras
- A combinatorial model for crystals of Kac-Moody algebras
- Canonical Bases Arising from Quantized Enveloping Algebras. II
- Affine Weyl Groups in K-Theory and Representation Theory
- Introduction to quantum groups
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