Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Okuyama's theorems about Alvis-Curtis duality   The purpose of this paper is to report on the unpublished manuscript [O] by
T. Okuyama where are proved some conjectures generalizing to homotopy
categories the theorems of [CaRi] and [LS] holding in derived categories. We
refer to the latter references and [CaEn]~\S 4 for a broader introduction to
the subject.
  The main theme is the one of complexes related with the Coxeter complex and
the action of parabolic subgroups on them, either for finite groups with
BN-pairs or for finite dimensional Hecke algebras. Okuyama's contractions prove
a quite efficient tool in a number of situations (see the proof of Solomon-Tits
theorem in \S~6).
  We often stray away from Okuyama's proofs when it allows simplifications.

14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph