Abstract
For each n ≥3, we construct an uncountable family of models of the crystal of the basic \(U_{q}(\widehat {\mathfrak {sl}}_{n})\)-module. These models are all based on partitions, and include the usual n-regular and n-restricted models, as well as Berg’s ladder crystal, as special cases.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Berg, C.: (l,0)-JM partitions and a ladder based model for the basic crystal of \(\widehat{\mathfrak{sl}_{l}}\). arXiv:0901.3565 [math.CO]
Danilov, V., Karzanov, A., Koshevoy, G.: Combinatorics of regular A 2-crystals. J. Algebra 310, 218–234 (2007)
Grojnowski, I.: Affine \(\widehat {\mathfrak {sl}}_{p}\) controls the representation theory of the symmetric group and related Hecke algebras. arXiv:math/9907129
Kang, S.-J., Kashiwara, M., Misra, K., Miwa, T., Nakashima, T., Nakayashiki, A.: Affine crystals and vertex models. Int. J. Mod. Phys. 7(Supp. 1A), 449–484 (1992)
Kashiwara, M.: On crystal bases of the q-analogue of universal enveloping algebras. Duke Math. J. 63, 465–516 (1991)
Kashiwara, M.: Bases cristallines des groupes quantiques. Cours spécialisées, vol. 9. Société Mathématique de France, Paris (2002)
Misra, K., Miwa, T.: Crystal base for the basic representation of \(U_{q}(\widehat {\mathfrak{sl}}(n))\). Commun. Math. Phys. 134, 79–88 (1990)
Mullineux, G.: Bijections on p-regular partitions and p-modular irreducibles of the symmetric groups. J. Lond. Math. Soc. 20(2), 60–66 (1979)
Stembridge, J.: A local characterization of simply-laced crystals. Trans. Am. Math. Soc. 355, 4807–4823 (2003)
Tingley, P.: Monomial crystals and partition crystals. arXiv:0909.2242
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Fayers, M. Partition models for the crystal of the basic \(U_{q}(\widehat {\mathfrak{sl}}_{n})\)-module. J Algebr Comb 32, 339–370 (2010). https://doi.org/10.1007/s10801-010-0217-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10801-010-0217-9