On the decomposition matrices of the quantized schur algebra

Duke Mathematical Journal

Volumn 100, Issue 2, 1999, Pages 267-297

  Varagnolo, Michela ^a   Vasserot, Eric ^a  

^a UNIVERSITÉ DE CERGY PONTOISE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033570875     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-99-10010-X     Document Type: Article

References (26)

1. S. Ariki, On the decomposition numbers of the Hecke algebra of G(m, 1, n), J. Math. Kyoto Univ. 36 (1996), 789-808.
2. V. Chari and A. Pressley, A Guide to Quantum Groups, Cambridge Univ. Press, Cambridge, 1994.
3. V. Deodhar, On some geometric aspects of Bruhat orderings, II: The parabolic analogue ofKazhdan-Lusztigpolynomials, J. Algebra 111 (1987), 483-506.
4. J. Du, A note on quantized Weyl reciprocity at roots of unity, Algebra Colloq. 2 (1995), 363-372.
5. n, Internat. Math. Res. Notices 1993, 67-85.
6. J. A. Green, Hall algebras, hereditary algebras and quantum groups, Invent. Math. 120 (1995), 361-377.
7. R. M. Green, The affine q -Schur algebra, available from http://xxx.lanl.gov/abs/q-alg/9705015.
8. T. Hayashi, q-analogues of Clifford and Weyl algebras—spinor and oscillator representations of quantum enveloping algebras, Comm. Math. Phys. 127 (1990), 129-144.
9. N. Iwahori and H. Matsumoto, On some Bruhat decomposition and the structure of the Hecke rings of p-adic Chevalley groups, Inst. Hautes Etudes Sci. Publ. Math. 25 (1965), 5-48.
10. M. Kashiwara, T. Miwa, and E. Stern, Decomposition ofq -deformedFock spaces, Selecta Math. (N.S.) 1 (1995), 787-805.
11. M. Kashiwara and T. Tanisaki, Kazhdan-Lusztig conjecture for affine Lie algebras with negative level, Duke Math. J. 77 (1995), 21-62.
12. D. Kazhdan and G. Lusztig, Tensor structures arising from affine Lie algebras, I, J. Amer. Math. Soc. 6 (1993), 905-947
13. D. Kazhdan and G. Lusztig, Tensor structures arising from affine Lie algebras, II, J. Amer. Math. Soc, 949-1011
14. D. Kazhdan and G. Lusztig, Tensor structures arising from affine Lie algebras, III, J. Amer. Math. Soc. 7 (1994), 335-381
15. D. Kazhdan and G. Lusztig, Tensor structures arising from affine Lie algebras, IV, J. Amer. Math. Soc, 383-453.
16. B. Leclerc and J.-Y. Thibon, Canonical bases of q -deformed Fock spaces, Internat. Math. Res. Notices 1996, 447-456.
17. G. Lusztig, Canonical bases arising from quantized enveloping algebras, J. Amer. Math. Soc. 3 (1990), 447-498.
18. G. Lusztig, Quivers, perverse sheaves, and quantized enveloping algebras, J. Amer. Math. Soc. 4 (1991), 365-421.
19. G. Lusztig, Introduction to Quantum Groups, Progr. Math. 110, Birkhauser, Boston, 1993.
20. G. Lusztig, “Canonical bases and Hall algebras” in Representation Theories and Algebraic Geometry (Montreal, PQ, 1997), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 514, Kluwer, Dordrecht, 1998, 365-399.
21. q(sl(n)), Comm. Math. Phys. 134 (1990), 79-88.
22. H. Nakajima, Instantons on ALE spaces, quiver varieties, and Kac-Moody algebras, Duke Math. J. 76 (1994), 365-416.
23. O. Schiffmann, Algèbres affines quantiques aux racines de l'unité et K-théorie équivari-ante, C. R. Acad. Sci. Paris Sér. I Math. 327 (1998), 433-438.
24. M. Varagnolo and E. Vasserot, Double-loop algebras and the Fock space, Invent. Math. 133 (1998), 133-159.
25. E. Vasserot, Représentations de groupes quantiques et permutations, Ann. Sci. École Norm. Sup. (4) 26 (1993), 747-773.
26. E. Vasserot, Affine quantum groups and equivariant K-theory, Transform. Groups 3 (1998), 269-299.