A characterization of the modular representations of finite groups with split (B, N)-pairs

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tET IE=EndrG(Y ) and Y=YI|174 be a decomposition of Y into a non-zero indecomposable submodules. The purpose of this paper is to state a characteristic of irreducible modular representations of G over K, i.e., the existence of intrinsic bijective correspondences among the set of all equivalence classes of irreducible KG-modules, the set {Y1, ..., Y~} and the set of all equivalence classes of irreducible representations of IE, which are all one-dimensional and determine the weights of the corresponding irreducible KG-modules. More precisely speaking, let ~b be a corresponding root system of the Weyl group W=N/Bc~N with a base A = {c~1, ..., ct~}. Let U1, ..., U, and Hi, ..., H, be certain subgroups of U and H = B c~ N respectively suffixed by the same i's of ei's. Then it is shown that IE is generated by {Ah,A(w~)[heH, wieR } where (wi)'s are certain coset representatives of R in N and

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詳細情報 詳細情報について

  • CRID
    1871146593073344384
  • DOI
    10.1007/bf01322605
  • ISSN
    14321823
    00255874
  • データソース種別
    • OpenAIRE

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