Branching functions of A (1)n-1 and Jantzen-Seitz problem for Ariki-Koike algebras

Advances in Mathematics

Volumn 141, Issue 2, 1999, Pages 322-365

  Foda, Omar ^a   Leclerc, Bernard ^b   Okado, Masato ^c   Thibon, Jean Yves ^d   Welsh, Trevor A ^a  

^a UNIVERSITY OF MELBOURNE   (Australia)

^b UNIVERSITÉ DE CAEN   (France)

^c OSAKA UNIVERSITY   (Japan)

^d Université de Marne la Vallée   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033540585     PISSN: 00018708     EISSN: None     Source Type: Journal    
DOI: 10.1006/aima.1998.1783     Document Type: Article

References (33)

1. G. E. Andrews, R. J. Baxter, and P. J. Forrester, Eight-vertex SOS model generalized Rogers-Ramanujan-type identities, J. Stat. Phys. 35 (1984), 193-266.
2. n, J. Algebra 169 (1994), 216-225.
3. S. Ariki, On the decomposition numbers of the Hecke algebra of G(m, 1, n), J. Math. Kyoto Univ. 36 (1996), 789-808.
4. n and construction of its irreducible representations, Adv. Math. 106 (1994), 216-243.
5. M. Broué and G. Malle, Zyklotomische Heckealgebren, Asterisque 212 (1993), 119-189.
6. E. Date, M. Jimbo, A. Kuniba, T. Miwa, and M. Okado, Paths, Maya diagrams, and representations of s-fraktur signI-fraktur sign (r, C), Adv. Stud. Pure Math. 19 (1989), 149-191.
7. R. Dipper and G. D. James, Representations of Hecke algebras of general linear groups, Proc. London Math. Soc. 52 (1986), 20-52.
8. R. Dipper and G. D. James, Blocks and idempotents of Hecke algebras of general linear groups, Proc. London Math. Soc. 54 (1987), 57-82.
9. n at roots of unity, Proc. London Math. Soc. 70 (1995), 505-528.
10. O. Foda, B. Leclerc, M. Okado, J.-Y. Thibon, and T. A. Welsh, RSOS models and Jantzen-Seitz representations of Hecke algebras, Lett. Math. Phys. 43 (1998), 31-42.
11. O. Foda, B. Leclerc, M. Okado, J.-Y. Thibon, and T. A. Welsh, Combinatorics of sovable lattice models, and modular representations of Hecke algebras, in "Geometric Analysis and Lie Theory in Mathematics and Physics," Lecture Notes Series of The Austr. Math. Soc. 11 (1998), 243-290.
12. 2, J. Math. Phys. 37 (1996), 965-986.
13. J. Graham and G. Lehrer, Cellular algebras, Invent. Math. 123 (1996), 1-34.
14. G. D. James and A. Kerber, "The Representation Theory of The Symmetric Group," Addison-Wesley, Reading, MA, 1981.
15. J. C. Jantzen and G. M. Seitz, On the representation theory of the symmetric groups, Proc. London Math. Soc. 65 (1992), 475-504.
16. q(S-farktur signl (n)) at q = 0, Commun. Math. Phys. 136 (1991), 543-566.
17. n-1 family, Nucl. Phys. B 300 (1988), 74-108.
18. V. Kac, "Infinite Dimensional Lie Algebras," 3rd ed., Cambridge Univ. Press, Cambridge, UK, 1990.
19. V. Kac and D. H. Peterson, Infinite-dimensional Lie algebras, Theta functions and modular forms, Adv. Math. 53 (1984), 125-264.
20. S.-J. Kang, M. Kashiwara, K. C. Misra, T. Miwa, T. Nakashima, and A. Nakayashiki, Affine crystals and vertex models, Int. J. Mod. Phys. A 7 (1A) (1992), 449-484.
21. S.-J. Kang, M. Kashiwara, K. C. Misra, T. Miwa, T. Nakashima, and A. Nakayashiki, Perfect crystals of quantum affine Lie algebras, Duke Math. J. 68 (1992), 499-607.
22. M. Kashiwara, Crystalizing the q-analogue of universal enveloping algebras, Commun. Math. Phys. 133 (1990), 249-260.
23. M. Kashiwara, On crystal bases of the q-analogue of universal enveloping algebras, Duke Math. J. 63 (1991), 465-516.
24. M. Kashiwara, Global crystal bases of quantum groups, Duke Math. J. 69 (1993), 455-485.
25. A. S. Kleshchev, Branching rules for the modular representations of symmetric groups III; some corollaries and a problem of Mullineux, J. London Math. Soc. 54 (1996), 25-38.
26. A. Lascoux, B. Leclerc, and J.-Y. Thibon, Une confecture pour le calcul des matrices de décomposition des algèbres de Hecke de type A aux racines de l'unité, C. R. Acad. Sci. Paris 321 (1995), 511-516.
27. A. Lascoux, B. Leclerc, and J.-Y. Thibon, Hecke algebras at roots of unity and crystal bases of quantum affine algebras, Commun. Math. Phys. 181 (1996), 205-263.
28. A. Lascoux and M.-P. Schützenberger, Symmetrization operators on polynomial rings, Funct. Anal. Appl. 21 (1987), 77-78.
29. B. Leclerc and J.-Y. Thibon, Canonical bases of q-deformed Fock spaces, Internat. Math. Res. Notices 9 (1996), 447-456.
30. G. Lusztig, Equivariant K-theory and representations of Hecke algebras, Proc. Amer. Math. Soc. 94 (1985), 337-342.
31. A. Mathas, Canonical Bases and the Decomposition Matrices of Ariki-Koike Algebras, preprint, 1996.
32. A. Mathas, Simple modules of Ariki-Koike algebras, Proc. Sym. Pure Math., to appear (1997).
33. n), Commun. Math. Phys. 134 (1990), 79-88.