The modular representation theory of $q$-Schur algebras
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- by Jie Du PDF
- Trans. Amer. Math. Soc. 329 (1992), 253-271 Request permission
Abstract:
We developed some basic theory of characteristic zero modular representations of $q$-Schur algebras. We described a basis of the $q$-Schur algebra in terms of the relative norm which was first introduced by P. Hoefsmit and L. Scott, and studied the product of two such basis elements. We also defined the defect group of a primitive idempotent in a $q$-Schur algebra and showed that such a defect group is just the vertex of the corresponding indecomposable ${\mathcal {H}_F}$-module.References
- Jie Du, The Green correspondence for the representations of Hecke algebras of type $A_{r-1}$, Trans. Amer. Math. Soc. 329 (1992), no.Β 1, 273β287. MR 1022164, DOI 10.1090/S0002-9947-1992-1022164-1
- Richard Dipper and Gordon James, Representations of Hecke algebras of general linear groups, Proc. London Math. Soc. (3) 52 (1986), no.Β 1, 20β52. MR 812444, DOI 10.1112/plms/s3-52.1.20
- Richard Dipper and Gordon James, Blocks and idempotents of Hecke algebras of general linear groups, Proc. London Math. Soc. (3) 54 (1987), no.Β 1, 57β82. MR 872250, DOI 10.1112/plms/s3-54.1.57
- Richard Dipper and Gordon James, The $q$-Schur algebra, Proc. London Math. Soc. (3) 59 (1989), no.Β 1, 23β50. MR 997250, DOI 10.1112/plms/s3-59.1.23
- Richard Dipper and Gordon James, $q$-tensor space and $q$-Weyl modules, Trans. Amer. Math. Soc. 327 (1991), no.Β 1, 251β282. MR 1012527, DOI 10.1090/S0002-9947-1991-1012527-1
- V. G. Drinfelβ²d, Quantum groups, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986) Amer. Math. Soc., Providence, RI, 1987, pp.Β 798β820. MR 934283
- Walter Feit, The representation theory of finite groups, North-Holland Mathematical Library, vol. 25, North-Holland Publishing Co., Amsterdam-New York, 1982. MR 661045
- J. A. Green, Blocks of modular representations, Math. Z. 79 (1962), 100β115. MR 141717, DOI 10.1007/BF01193108 β, Polynomial representations of $G{L_n}$, Lecture Notes in Math., vol. 830, Springer-Verlag, 1980.
- Michio Jimbo, A $q$-analogue of $U({\mathfrak {g}}{\mathfrak {l}}(N+1))$, Hecke algebra, and the Yang-Baxter equation, Lett. Math. Phys. 11 (1986), no.Β 3, 247β252. MR 841713, DOI 10.1007/BF00400222 L. Jones, Centers of generic algebras, Ph. D. Thesis, Univ. of Virginia, 1987.
- G. Lusztig, Modular representations and quantum groups, Classical groups and related topics (Beijing, 1987) Contemp. Math., vol. 82, Amer. Math. Soc., Providence, RI, 1989, pp.Β 59β77. MR 982278, DOI 10.1090/conm/082/982278
- L. L. Scott, Modular permutation representations, Trans. Amer. Math. Soc. 175 (1973), 101β121. MR 310051, DOI 10.1090/S0002-9947-1973-0310051-1
Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 329 (1992), 253-271
- MSC: Primary 20C30; Secondary 16G99, 20G40
- DOI: https://doi.org/10.1090/S0002-9947-1992-1022165-3
- MathSciNet review: 1022165