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Modular generalized Springer correspondence III: exceptional groups
We complete the construction of the modular generalized Springer
correspondence for an arbitrary connected reductive group, with a uniform proof
of the disjointness of induction series that avoids the case-by-case arguments
for classical groups used in previous papers in the series. We show that the
induction series containing the trivial local system on the regular nilpotent
orbit is determined by the Sylow subgroups of the Weyl group. Under some
assumptions, we give an algorithm for determining the induction series
associated to the minimal cuspidal datum with a given central character. We
also provide tables and other information on the modular generalized Springer
correspondence for quasi-simple groups of exceptional type, including a
complete classification of cuspidal pairs in the case of good characteristic,
and a full determination of the correspondence in type .Comment: 40 pages. Version 2: added section 7.5, modified Table 5.2 to match
current conventions of GAP3. Version 3 has minor edits suggested by the
referee, including a slight strengthening of Proposition 3.2; final version,
to appear in Math. Annale
Spectral transfer morphisms for unipotent affine Hecke algebras
In this paper we will give a complete classification of the spectral transfer
morphisms between the unipotent affine Hecke algebras of the various inner
forms of a given quasi-split absolutely simple algebraic group, defined over a
non-archimidean local field and split over an unramified extension
of . As an application of these results, the results of [O4] on the
spectral correspondences associated with such morphisms and some results of
Ciubotaru, Kato and Kato [CKK] we prove a conjecture of Hiraga, Ichino and
Ikeda [HII] on the formal degrees and adjoint gamma factors for all unipotent
discrete series characters of unramified simple groups of adjoint type defined
over .Comment: 61 pages; We explained the comparison with Lusztig's parameterization
of unipotent representations in more detai
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