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@PHDTHESIS{Neunhffer:58877,
      author       = {Neunhöffer, Max},
      othercontributors = {Hiß, Gerhard},
      title        = {{U}ntersuchungen zu {J}ames' {V}ermutung über
                      {I}wahori-{H}ecke-{A}lgebren vom {T}yp {A}},
      address      = {Aachen},
      publisher    = {Publikationsserver der RWTH Aachen University},
      reportid     = {RWTH-CONV-120704},
      pages        = {150 S.},
      year         = {2003},
      note         = {Aachen, Techn. Hochsch., Diss., 2003},
      abstract     = {This thesis deals with a conjecture by Gordon James from
                      1990 and a variant by Meinolf Geck about decomposition maps
                      of the generic Iwahori-Hecke algebra H of the symmetric
                      group on n points arising from specialization to
                      characteristic l>0. If the parameter of the algebra is
                      specialized to an element q of GF(l) with multiplicative
                      order e, the conjecture states, that, for el>n, the
                      decomposition map does not depend on l and q, but only on e.
                      The main result of the present work is the following
                      reformulation of the James-Geck conjecture: For el>n every
                      primitive idempotent in the extension of scalars AH is
                      primitive as idempotent in the algebra A'H, where A and A'
                      are rings of characteristic 0 (which are explicitly
                      constructed for l and q), such that A is contained in A' and
                      therefore AH in A'H. Thus an equivalent statement is given,
                      which contains only rings and algebras of characteristic 0.
                      To prove equivalence, generalizations of the well-known
                      methods of lifting of idempotents and of Brauer reciprocity
                      are developed. In addition results and observations are
                      presented, that might lead to an approach to a proof of the
                      above mentioned reformulation. A method is presented, how
                      one can derive explicit formulae for primitive idempotents
                      in non-semi-simple symmetric algebras using matrix
                      representations on projective indecomposable modules. Such
                      matrix representations seem to arise naturally from the
                      Kazhdan-Lusztig cell modules. Another possible attack for a
                      proof stems from another result of the present thesis, an
                      explicit construction of a Wedderburn decomposition for H
                      using the Kazhdan-Lusztig basis.},
      cin          = {100000},
      ddc          = {510},
      cid          = {$I:(DE-82)100000_20140620$},
      typ          = {PUB:(DE-HGF)11},
      urn          = {urn:nbn:de:hbz:82-opus-5634},
      url          = {https://publications.rwth-aachen.de/record/58877},
}