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The Green correspondence for the representations of Hecke algebras of type $ A\sb {r-1}$


Author: Jie Du
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
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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 [Enhancements On Off] (What's this?)

  • [A1] J. L. Alperin, Local representation theory, Cambridge Univ. Press, 1986. MR 860771 (87i:20002)
  • [Du] Jie Du, The modular representation theory of $ q$-Schur algebras, Trans. Amer. Math. Soc. 329 (1992), 253-271. MR 1022165 (92g:20022)
  • [DJ1] R. Dipper and G. James, Representations of Hecke algebras of general linear groups, Proc. London Math. Soc. 52 (1986), 20-52. MR 812444 (88b:20065)
  • [DJ2] -, Blocks and idempotents of Hecke algebras of general linear groups, Proc. London Math. Soc. 53 (1987), 57-82. MR 872250 (88m:20084)
  • [DJ3] -, The $ q$-Schur algebras, Proc. London Math. Soc. 59 (1989), 23-50. MR 997250 (90g:16026)
  • [DJ4] -, $ q$-tensor spaces and $ q$-Weyl modules, Trans. Amer. Math. Soc. 327 (1991), 251-282. MR 1012527 (91m:20061)
  • [F] W. Feit, The representation theory of finite groups, North-Holland Mathematical Library, vol. 25, North-Holland, 1982. MR 661045 (83g:20001)
  • [G] J. A. Green, Blocks of modular representations, Math. Z. 79 (1962), 100-115. MR 0141717 (25:5114)
  • [G1] -, Polynomial representations of $ G{L_n}$, Lecture Notes in Math., vol. 830, Springer-Verlag, Berlin and New York, 1980.
  • [Ho] 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.
  • [Jo] L. Jones, Centers of generic algebras, Ph.D. Thesis, Univ. of Virginia, 1987.
  • [S] L. Scott, Modular permutation representations, Trans. Amer. Math. Soc. 175 (1973), 101-121. MR 0310051 (46:9154)
  • [Sh] Jianyi Shi, A result on the Bruhat order of a Coxeter group, J. Algebra (to appear). MR 1036406 (90k:20059)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1992-1022164-1
Keywords: Hecke algebra, relative norm, relatively projective, vertex, Green correspondence
Article copyright: © Copyright 1992 American Mathematical Society

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