A local characterization of simply-laced crystals
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- by John R. Stembridge PDF
- Trans. Amer. Math. Soc. 355 (2003), 4807-4823 Request permission
Abstract:
We provide a simple list of axioms that characterize the crystal graphs of integrable highest weight modules for simply-laced quantum Kac-Moody algebras.References
- Arkady Berenstein and Andrei Zelevinsky, Tensor product multiplicities, canonical bases and totally positive varieties, Invent. Math. 143 (2001), no. 1, 77–128. MR 1802793, DOI 10.1007/s002220000102
- Anthony Joseph, Quantum groups and their primitive ideals, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 29, Springer-Verlag, Berlin, 1995. MR 1315966, DOI 10.1007/978-3-642-78400-2
- Peter Littelmann, A Littlewood-Richardson rule for symmetrizable Kac-Moody algebras, Invent. Math. 116 (1994), no. 1-3, 329–346. MR 1253196, DOI 10.1007/BF01231564
- Peter Littelmann, Paths and root operators in representation theory, Ann. of Math. (2) 142 (1995), no. 3, 499–525. MR 1356780, DOI 10.2307/2118553
- Peter Littelmann, Crystal graphs and Young tableaux, J. Algebra 175 (1995), no. 1, 65–87. MR 1338967, DOI 10.1006/jabr.1995.1175
- P. Littelmann, Cones, crystals, and patterns, Transform. Groups 3 (1998), no. 2, 145–179. MR 1628449, DOI 10.1007/BF01236431
- Seok-Jin Kang, Masaki Kashiwara, Kailash C. Misra, Tetsuji Miwa, Toshiki Nakashima, and Atsushi Nakayashiki, Affine crystals and vertex models, Infinite analysis, Part A, B (Kyoto, 1991) Adv. Ser. Math. Phys., vol. 16, World Sci. Publ., River Edge, NJ, 1992, pp. 449–484. MR 1187560, DOI 10.1142/s0217751x92003896
- Masaki Kashiwara and Toshiki Nakashima, Crystal graphs for representations of the $q$-analogue of classical Lie algebras, J. Algebra 165 (1994), no. 2, 295–345. MR 1273277, DOI 10.1006/jabr.1994.1114
- Masaki Kashiwara, Crystal bases of modified quantized enveloping algebra, Duke Math. J. 73 (1994), no. 2, 383–413. MR 1262212, DOI 10.1215/S0012-7094-94-07317-1
- Masaki Kashiwara, On crystal bases, Representations of groups (Banff, AB, 1994) CMS Conf. Proc., vol. 16, Amer. Math. Soc., Providence, RI, 1995, pp. 155–197. MR 1357199
- Masaki Kashiwara, Similarity of crystal bases, Lie algebras and their representations (Seoul, 1995) Contemp. Math., vol. 194, Amer. Math. Soc., Providence, RI, 1996, pp. 177–186. MR 1395599, DOI 10.1090/conm/194/02393
- J. R. Stembridge, Combinatorial models for Weyl characters, Advances in Math. 168 (2002), 96–131.
Additional Information
- John R. Stembridge
- Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109–1109
- Received by editor(s): February 12, 2002
- Published electronically: July 24, 2003
- Additional Notes: This research was partially supported by NSF Grant DMS–0070685 and the Guggenheim Foundation.
- © Copyright 2003 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 355 (2003), 4807-4823
- MSC (2000): Primary 17B37, 05E99
- DOI: https://doi.org/10.1090/S0002-9947-03-03042-3
- MathSciNet review: 1997585