Quantum linear groups and representations of gln(double-struck F sign q)

Memoirs of the American Mathematical Society

Volumn , Issue 706, 2001, Pages 1-112

  Brundan, Jonathan ^a   Dipper, Richard ^a   Kleshchev, Alexander ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035218120     PISSN: 00659266     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (71)

1. [Ac] B. Ackermann, Erweiterte Howlett-Lehrer Theorie, Diploma thesis, Universität Stuttgart, 1999.
2. [AF] F. W. Anderson and K. R. Fuller, Rings and categories of modules, Springer-Verlag, 1974.
3. [A] M. Auslander, Representation theory of Artin algebras I, Comm. Algebra 1 (1974), 177-268.
4. n, Duke Math. J. 61 (1990), 655-677.
5. [B] M. Broué, Isométries de caractères et équivalences de Morita ou dérivées, Publ. Math. IHES 71 (1990), 45-63.
6. [BM] M. Broué and J. Michel, Blocs et series de Lusztig dans un groupe réductif fini, J. reine angew. Math. 395 (1989), 56-67.
7. n(q) and the forgotten basis of the Hall algebra, preprint, University of Oregon, 1999.
8. 1] J. Brundan and A. Kleshchev, Modular Littlewood-Richardson coefficients, Math. Z. 232 (1999), 287-320.
9. 2] J. Brundan and A. Kleshchev, Lower bounds for degrees of irreducible Brauer characters of finite general linear groups, J. Algebra, to appear.
10. [C] R. W. Carter, Finite groups of Lie type: conjugacy classes and complex characters, Wiley, New York, 1985.
11. [C1] G. Cliff, A tensor product theorem for quantum linear groups at even roots of unity, J. Algebra 165 (1994), 566-575.
12. 1] E. Cline, B. Parshall and L. Scott, Derived categories and Morita theory, J. Algebra 104 (1986), 397-409.
13. 2] E. Cline, B. Parshall and L. Scott, Finite dimensional algebras and highest weight categories, J. reine angew. Math. 391 (1988), 85-99.
14. 3] E. Cline, B. Parshall and L. Scott, Generic and q-rational representation theory, Publ. RIMS Kyoto Univ. 35 (1999), 31-90.
15. [DL] P. Deligne and G. Lusztig, Representations of reductive groups over finite fields, Annals of Math. 103 (1976), 103-161.
16. 1] F. Digne and J. Michel, Foncteurs de Lusztig et caractères des groupes linéaires et unitaires sur un corps fini, J. Algebra 107 (1987), 217-255.
17. 2] F. Digne and J. Michel, Representations of finite groups of Lie type, LMS Student Texts no. 21, Cambridge University Press, 1991.
18. 1] R. Dipper, On the decomposition numbers of finite general linear groups, Trans. Amer. Math. Soc. 290 (1985), 315-344.
19. 2] R. Dipper, On the decomposition numbers of finite general linear groups II. Trans. Amer. Math. Soc. 292 (1985), 123-133.
20. 3] R. Dipper, On quotients of Hom functors and representations of finite general linear groups I, J. Algebra 130 (1990), 235-259.
21. 4] R. Dipper, On quotients of Hom functors and representations of finite general linear groups II, J. Algebra 209 (1998), 199-269.
22. n, Proc. London Math. Soc. 63 (1991), 165-211.
23. 1] R. Dipper and J. Du, Harish-Chandra vertices, J. reine angew. Math.437 (1993), 101-130.
24. 2] R. Dipper and J. Du, Harish-Chandra vertices and Steinberg's tensor product theorem for general linear groups in non-describing characteristic, Proc. London Math.Soc. 75 (1997), 559-599.
25. [DF] R. Dipper and P. Fleischmann, Modular Harish-Chandra theory I, Math. Z. 211 (1992), 49-71.
26. 1] R. Dipper and G. James, Representations of Hecke algebras of general linear groups, Proc. London Math. Soc. 52 (1986), 20-52.
27. n(q), J. Algebra 104 (1986), 266-288.
28. 3] R. Dipper and G. James, The q-Schur algebra, Proc. London Math. Soc. 59 (1989), 23-50.
29. 4] R. Dipper and G. James, q-Tensor space and q-Weyl modules, Trans. Amer. Math. Soc. 327 (1991), 251-282.
30. [DR] V. Dlab and C. M. Ringel, Quasi-hereditary algebras, Illinois J. Math. 33 (1989), 280-291.
31. 1] S. Donkin, Hopf complements and injective comodules for algebraic groups, Proc. London Math. Soc. 40 (1980), 298-319.
32. 2] S. Donkin, Finite resolutions of modules for reductive algebraic groups, J. Algebra 101 (1986), 473-488.
33. 3] S. Donkin, On Schur algebras and related algebras I, J. Algebra 104 (1986), 310-328.
34. 4] S. Donkin, On Schur algebras and related algebras II J. Algebra 111 (1987), 354-364.
35. 5] S. Donkin, On tilting modules for algebraic groups, Math. Z. 212 (1993), 39-60.
36. n, J. Algebra 181 (1996), 235-266.
37. 7] S. Donkin, The q-Schur algebra, LMS Lecture Notes no. 253, Cambridge University Press, 1998.
38. [Du] J. Du, A note on quantized Weyl reciprocity at roots of unity, Alg. Colloq. 2 (1995), 363-372.
39. [FS] P. Fong and B. Srinavasan, The blocks of finite general linear and unitary groups, Invent. Math. 69 (1982), 109-153.
40. [GH] M. Geck and G. Hiss, Basic sets of Brauer characters of finite groups of Lie type, J. reine angew. Math. 418 (1991), 173-188.
41. [Ge] S. I. Gelfand, Representations of the full linear group over a finite field, Math. USSR Sbornik 12 (1970), 13-39.
42. [GG] I. M. Gelfand and M.I. Graev, The construction of irreducible representations of simple algebraic groups over a finite field, Dokl. Akad. Nauk USSR 147 (1962), 529-532.
43. 1] J. A. Green, The characters of the finite general linear groups, Trans. Amer. Math. Soc. 80 (1955), 402-447.
44. n, Lecture Notes in Math., vol. 830, Springer-Verlag, 1980.
45. [Gr] R. M. Green, q-Schur algebras and quantized enveloping algebras, PhD thesis, Warwick University, 1995.
46. [GT] R. Guralnick and Pham Huu Tiep, Low-dimensional representations of special linear groups in cross characteristics, Proc. London Math. Soc. 78 (1999), 116-138.
47. 1] R. Howlett and G. Lehrer, Induced cuspidal representations and generalized Hecke rings, Invent. Math. 58 (1980), 37-64.
48. 2] R. Howlett and G. Lehrer, On Harish-Chandra induction for modules of Levi subgroups, J. Algebra 165 (1994), 172-183.
49. [HR] D. Happel and C. M. Ringel, Tilted algebras, Trans. Am. Math. Soc. 276 (1982), 399-443.
50. 1] G. James, Representations of general linear groups, LMS Lecture Notes no. 94, Cambridge University Press, 1984.
51. 2] G. James, The irreducible representations of the finite general linear groups, Proc. London Math. Soc. 52 (1986), 236-268.
52. [JM] G. James and A. Mathas, A q-analogue of the Jantzen-Schaper theorem, Proc. London Math. Soc. 74 (1997), 241-274.
53. [Ja] J. C. Jantzen, Representations of Algebraic Groups, Academic Press, Orlando, 1987.
54. [JS] J. C. Jantzen and G. M. Seitz, On the representation theory of the symmetric groups, Proc. London Math. Soc. 65 (1992), 475-504.
55. [Ka] G. Karpilovsky, Group representations, vol. 4, Math. Studies no. 182, North-Holland, Amsterdam, 1995.
56. [KK] M. Klucznik and S. König, Characteristic tilting modules over quasi-hereditary algebras, Lecture Notes, University of Bielefeld, 1999.
57. [La] P. Landrock, Finite Group Algebras and their Modules, Cambridge University Press, 1983.
58. 1] G. Lusztig, On the finiteness of the number of unipotent classes, Invent. Math. 34 (1976), 201-213.
59. 2] G. Lusztig, Finite dimensional Hopf algebras arising from quantized universal enveloping algebras, J. Amer. Math. Soc. 3 (1990), 257-297.
60. [LS] G. Lusztig and B. Srinivasan, The characters of the finite unitary groups, J. Algebra 49 (1977), 167-171.
61. [M] I. G. Macdonald, Symmetric functions and Hall polynomials, Oxford Mathematical Monographs, second edition, OUP, 1995.
62. [Ma] A. Mathas, Hecke algebras and Schur algebras of the symmetric group, Lec; ture notes, Universität Bielefeld, 1998.
63. n, Comment. Math. Helv. 74 (1999), 280-296.
64. [PW] B. Parshall and J.-P. Wang, Quantum linear groups, Mem. Amer. Math. Soc. 439 (1991).
65. [R] C. M. Ringel, The category of modules with good filtrations over a quasi-hereditary algebra has almost split sequences, Math. Z. 208 (1991), 209-225.
66. [S] V. Schubert, Durch den Hom-Funktor induzierte Äquivalenzen, PhD thesis, Universität Stuttgart, 1999.
67. [Se] J.-P. Serre, Linear representations of finite groups, Graduate Texts in Mathematics 42, Springer-Verlag, Berlin, 1977.
68. [Sw] M. Sweedler, Hopf algebras, Benjamin, New York, 1969.
69. n(q) and the q-Schur algebra, J. Math. Soc. Japan 48 (1996), 259-274.
70. [Th] E. Thoma, Die Einschränkung der Charactere von GL(n,q) auf GL(n-1,q), Math. Z. 119 (1971), 321-338.
71. [Z] A. Zelevinsky, Representations of finite classical groups, Lecture Notes in Math. 869, Springer-Verlag, Berlag, Berlin, 1981.