Diagram algebras, Hecke algebras and decomposition numbers at roots of unity
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 36 (2003) no. 4, pp. 479-524.
@article{ASENS_2003_4_36_4_479_0,
     author = {Graham, J. J. and Lehrer, G. I.},
     title = {Diagram algebras, {Hecke} algebras and decomposition numbers at roots of unity},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {479--524},
     publisher = {Elsevier},
     volume = {Ser. 4, 36},
     number = {4},
     year = {2003},
     doi = {10.1016/S0012-9593(03)00020-X},
     mrnumber = {2013924},
     zbl = {1062.20003},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/S0012-9593(03)00020-X/}
}
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Graham, J. J.; Lehrer, G. I. Diagram algebras, Hecke algebras and decomposition numbers at roots of unity. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 36 (2003) no. 4, pp. 479-524. doi : 10.1016/S0012-9593(03)00020-X. http://www.numdam.org/articles/10.1016/S0012-9593(03)00020-X/

[1] Ariki S., On the decomposition numbers of the Hecke algebra of G(m,1,n), J. Math. Kyoto Univ. 36 (4) (1996) 789-808. | MR | Zbl

[2] Ariki S., Mathas A., The number of simple modules of the Hecke algebras of type G(r,1,n), Math. Z., to appear. | MR | Zbl

[3] Benson D.J., Representations and Cohomology. I. Basic Representation Theory of Finite Groups and Associative Algebras, Cambridge Stud. Adv. Math., 30, Cambridge University Press, Cambridge, 1998. | MR | Zbl

[4] Bernstein I.N., Zelevinsky A.V., Induced representations of reductive p-adic groups, Ann. Sci. Éc. Norm. Sup. (4) 10 (1977) 441-472. | Numdam | MR | Zbl

[5] Chriss N., Ginzburg V., Representation Theory and Complex Geometry, Birkhäuser Boston, Boston, MA, 1997. | MR | Zbl

[6] Cox A., Graham J.J., Martin P., The blob algebra in positive characteristic, Preprint, 2001. | MR

[7] Deligne P., Les immeubles des groupes de tresses généralisés, Invent. Math. 17 (1972) 273-302. | MR | Zbl

[8] Fan C.K., Green R.M., On the affine Temperley-Lieb algebras, J. London Math. Soc. (2) 60 (1999) 366-380. | MR | Zbl

[9] Ginzburg V., Lagrangian construction of representations of Hecke algebras, Adv. in Math. 63 (1987) 100-112. | MR | Zbl

[10] Grojnowski I., Representations of affine Hecke algebras (and affine quantum GLn) at roots of unity, Internat. Math. Res. Notices 5 (1994). | MR | Zbl

[11] Green R.M., On representations of affine Temperley-Lieb algebras, in: Algebras and Modules II, CMS Conference Proceedings, 24, American Math. Society, Providence, RI, 1998, pp. 245-261. | MR | Zbl

[12] Geck M., Lambropoulou S., Markov traces and knot invariants related to Iwahori-Hecke algebras of type B, J. Reine Angew. Math. 482 (1997) 191-213. | MR | Zbl

[13] Graham J.J., Lehrer G.I., Cellular algebras, Invent. Math. 123 (1996) 1-34. | MR | Zbl

[14] Graham J.J., Lehrer G.I., The representation theory of affine Temperley-Lieb algebras, Enseign. Math. 44 (1998). | MR | Zbl

[15] Graham J.J., Lehrer G.I., The two-step nilpotent representations of the extended affine Hecke algebra of type A, Compositio Math. 133 (2002) 173-197. | MR | Zbl

[16] Jones V.F.R., A quotient of the affine Hecke algebra in the Brauer algebra, Enseign. Math. 40 (1994) 313-344. | MR | Zbl

[17] Jones V.F.R., Hecke algebra representations of braid groups and link polynomials, Ann. of Math. 126 (1987) 335-388. | MR | Zbl

[18] Jones V.F.R., Planar algebras, Preprint on server, 2001.

[19] Kazhdan D., Lusztig G., Proof of the Deligne-Langlands conjecture for Hecke algebras, Invent. Math. 87 (1987) 153-215. | MR | Zbl

[20] Lascoux A., Leclerc B., Thibon J.-Y., Hecke algebras at roots of unity and crystal bases of quantum affine algebras, Comm. Math. Phys. 181 (1996) 205-263. | MR | Zbl

[21] Leclerc B., Thibon J.-Y., Vasserot E., Zelevinsky's involution at roots of unity, J. Reine Angew. Math. 513 (1999) 33-51. | MR | Zbl

[22] Lusztig G., Some examples of square integrable representations of semisimple p-adic groups, Trans. Amer. Math. Soc. 277 (1983) 623-653. | MR | Zbl

[23] Lusztig G., Notes on affine Hecke algebras, Preprint, MIT, 2000. | MR

[24] Lusztig G., Affine Hecke algebras and their graded version, J. Amer. Math. Soc. 2 (1989) 599-635. | MR | Zbl

[25] Martin P.P., Woodcock D., On the structure of the blob algebra, J. Algebra 225 (2000) 957-988. | MR | Zbl

[26] Martin P., Saleur H., The blob algebra and the periodic Temperley-Lieb algebra, Lett. Math. Phys. 30 (1994) 189-206. | MR | Zbl

[27] Nguyen V.D., The fundamental groups of the spaces of regular orbits of the affine Weyl groups, Topology 22 (1983) 425-435. | MR | Zbl

[28] Rogawski J.D., On modules over the Hecke algebra of a p-adic group, Invent. Math. 79 (1985) 443-465. | MR | Zbl

[29] Tom Dieck T., Symmetrische Brücken und Knotentheorie zu den Dynkin-Diagrammen vom Typ B, J. Reine Angew. Math. 451 (1994) 71-88. | MR | Zbl

[30] Xi N., Representations of Affine Hecke Algebras, Lecture Notes in Math., 1587, Springer-Verlag, Berlin, 1994. | MR | Zbl

[31] Zelevinsky A.V., Induced representations of reductive p-adic groups. II. On irreducible representations of GL(n), Ann. Sci. Éc. Norm. Sup. 13 (1980) 165-210. | Numdam | MR | Zbl

[32] Zelevinsky A.V., The p-adic analogue of the Kazhdan-Lusztig conjecture, Funktsional. Anal. i Prilozhen. 15 (1981) 9-21, (Russian). | MR | Zbl

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