The Green correspondence for the representations of Hecke algebras of type $A_ {r-1}$
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Abstract:
We first prove the conjecture mentioned by Leonard K. Jones in his thesis. By applying this conjecture, we obtain that the vertex of an indecomposable ${\mathcal {H}_F}$-module is an $l$-parabolic subgroup. Finally, we establish the Green correspondence for the representations of Hecke algebras of type ${A_{r - 1}}$.References
- J. L. Alperin, Local representation theory, Cambridge Studies in Advanced Mathematics, vol. 11, Cambridge University Press, Cambridge, 1986. Modular representations as an introduction to the local representation theory of finite groups. MR 860771, DOI 10.1017/CBO9780511623592
- Jie Du, The modular representation theory of $q$-Schur algebras, Trans. Amer. Math. Soc. 329 (1992), no.ย 1, 253โ271. MR 1022165, DOI 10.1090/S0002-9947-1992-1022165-3
- Richard Dipper and Gordon James, Representations of Hecke algebras of general linear groups, Proc. London Math. Soc. (3) 52 (1986), no.ย 1, 20โ52. 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.ย 1, 57โ82. 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.ย 1, 23โ50. 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.ย 1, 251โ282. MR 1012527, DOI 10.1090/S0002-9947-1991-1012527-1
- 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), 100โ115. MR 141717, DOI 10.1007/BF01193108 โ, Polynomial representations of $G{L_n}$, Lecture Notes in Math., vol. 830, Springer-Verlag, Berlin and New York, 1980. P. Hoefsmit, Representations of Hecke algebras of finite groups with $(B,N)$-pairs of classical type, Ph.D. Dissertation, Univ. of British Columbia, Vancouver, 1974. L. Jones, Centers of generic algebras, Ph.D. Thesis, Univ. of Virginia, 1987.
- L. L. Scott, Modular permutation representations, Trans. Amer. Math. Soc. 175 (1973), 101โ121. MR 310051, DOI 10.1090/S0002-9947-1973-0310051-1
- Jian Yi Shi, A result on the Bruhat order of a Coxeter group, J. Algebra 128 (1990), no.ย 2, 510โ516. MR 1036406, DOI 10.1016/0021-8693(90)90038-P
Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 329 (1992), 273-287
- MSC: Primary 20C30; Secondary 16G99, 20G40
- DOI: https://doi.org/10.1090/S0002-9947-1992-1022164-1
- MathSciNet review: 1022164