Partition models for the crystal of the basic U q([^(\mathfrak sl)] n) U_{q}(\widehat {\mathfrak{sl}}_{n})-module
Matthew Fayers
DOI: 10.1007/s10801-010-0217-9
Abstract
For each n \geq 3, we construct an uncountable family of models of the crystal of the basic U q([^(\mathfrak sl)] n) 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.
Pages: 339–370
Keywords: keywords partition; highest-weight crystal
Full Text: PDF
References
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2. Danilov, V., Karzanov, A., Koshevoy, G.: Combinatorics of regular A2-crystals. J. Algebra 310, 218- 234 (2007)
3. Grojnowski, I.: Affine slp controls the representation theory of the symmetric group and related Hecke algebras.
4. 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)
5. Kashiwara, M.: On crystal bases of the q-analogue of universal enveloping algebras. Duke Math. J. 63, 465-516 (1991)
6. Kashiwara, M.: Bases cristallines des groupes quantiques. Cours spécialisées, vol.
9. Société Mathé- matique de France, Paris (2002)
7. Misra, K., Miwa, T.: Crystal base for the basic representation of Uq (sl(n)). Commun. Math. Phys. 134, 79-88 (1990)
8. Mullineux, G.: Bijections on p-regular partitions and p-modular irreducibles of the symmetric groups. J. Lond. Math. Soc. 20(2), 60-66 (1979)
9. Stembridge, J.: A local characterization of simply-laced crystals. Trans. Am. Math. Soc. 355, 4807- 4823 (2003)
10. Tingley, P.: Monomial crystals and partition crystals.
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