Split spetses for primitive reflection groups:
Gespeichert in:
| Beteiligte Personen: | , , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Paris
Soc. Math. de France
2014
|
| Schriftenreihe: | Astérisque
359 |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027219559&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027219559&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | VI, 146 S. |
| ISBN: | 9782856297810 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV041773629 | ||
| 003 | DE-604 | ||
| 005 | 20140430 | ||
| 007 | t| | ||
| 008 | 140402s2014 xx |||| 00||| eng d | ||
| 020 | |a 9782856297810 |9 978-2-85629-781-0 | ||
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| 084 | |a 20G05 |2 msc | ||
| 100 | 1 | |a Broué, Michel |d 1946- |e Verfasser |0 (DE-588)113828853 |4 aut | |
| 245 | 1 | 0 | |a Split spetses for primitive reflection groups |c Michel Broué ; Gunter Malle ; Jean Michel |
| 264 | 1 | |a Paris |b Soc. Math. de France |c 2014 | |
| 300 | |a VI, 146 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Astérisque |v 359 | |
| 700 | 1 | |a Malle, Gunter |d 1960- |e Verfasser |0 (DE-588)1016705093 |4 aut | |
| 700 | 1 | |a Michel, Jean |d ca. 20./21. Jh. |e Verfasser |0 (DE-588)1050184939 |4 aut | |
| 830 | 0 | |a Astérisque |v 359 |w (DE-604)BV002579439 |9 359 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027219559&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027219559&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |3 Klappentext |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-027219559 | |
Datensatz im Suchindex
| _version_ | 1819332602968932352 |
|---|---|
| adam_text | CONTENTS
From Weyl groups to complex reflection groups
......................... 1
1.
Reflection groups, braid groups,
Hecke
algebras
...................... 9
1.1.
Complex reflection groups and reflection cosets
.......................... 9
1.2.
Uniform class functions on a reflection coset
............................ 14
1.3.
Ф
-Sylow
theory and
Ф
-split
Levi
subcosets
.............................. 24
1.4.
The associated braid group
.............................................. 27
1.5.
The generic
Hecke
algebra
............................................... 30
1.6.
Ф
-cyclotomic
Hecke
algebras, Rouqmer blocks
........................... 35
2.
Complements on finite reductive groups
............................... 39
2.1.
Notation and hypothesis for finite reductive groups
..................... 39
2.2.
Deligne-Lusztig varieties attached to regular elements
................... 41
2.3.
On eigenvalues of Frobenius
............................................. 42
2.4.
Computing numbers of rational points
.................................. 44
2.5.
Some consequences of abelian defect group conjectures
.................. 45
2.6.
Actions of some braids
.................................................. 48
2.7.
Is there a stronger
Poincaré
duality?
.................................... 50
3.
Spetsial
Ф
-cyclotomic
Hecke
algebras
..............................___ 53
3.1.
Prerequisites and notation
................ .............................. 53
3-2.
Reduction to the cyclic case
............................................. 54
3.3.
Spetsial
Ф
-cyclotomic
Hecke
algebras at
χαψ
............................. 55
3.4.
More on spetsial
Ф
-cyclotomic
Hecke
algebras
........................... 62
3.5.
Spetsiai data at a regular element, spetsial groups
...................... 74
4.
Axioms for spetses
........................................................ 79
4.1.
Axioms used in
§6 ....................................................... 79
4.2.
Supplementary axioms for spetses
....................................... 85
CONTENTS
5. Determination
of Uch(G): the algorithm
............................... 89
5.1.
Determination of
Uch
(G)
................................................ 89
5.2.
The principal series Uch(G,
1) ........................................... 90
5.3.
The series Uch((G,
ξ)
for
ξ
e
ZW
........................................ 91
5.4.
An algorithm to determine some Uch(G,
ζ)
for
ζ
regular
................ 92
5.5.
An example of computational problems
................................. 93
5.6.
Determination of l-Harish-Chandra series
............................... 94
5.7.
Determination of families
................................................ 96
5.8.
The mam theorem
....................................................... 96
A. Tables
...................................................................... 99
A.I. Irreducible K~
су
clotomic polynomials
...................................100
A.
2.
Unipotent characters for Zz
.............................................101
A.3. Unipotent characters for Z^
.............................................101
A.
4.
Unipotent characters for G4
............................................101
A.
5.
Unipotent characters for Gq
............................................102
A.
6.
Unipotent characters for G%
............................................
ЮЗ
A.
7.
Unipotent characters for G14
...........................................104
A.
8.
Unipotent characters for
£3,1,2 .........................................
Ю7
Α.
9. Umpotent
characters for G24
...........................................107
A.
10.
Unipotent characters for G25
..........................................
Ю8
A.ll. Unipotent characters for G26
..........................................
Π0
A.
12.
Unipotent characters for G27
..........................................113
A.
13.
Unipotent characters for
(?з,з
3 ........................................116
A.
14.
Unipotent characters for
Gą^s
........................................116
A.
15.
Unipotent characters for G29
..........................................117
A.
16.
Unipotent characters for G32
..........................................
П9
A.I?. Unipotent characters for G33
..........................................126
A.
18.
Unipotent characters for C34
..........................................128
B. Errata for [BMM99]
.........................................................139
Bibliography
...................................................................141
Index
......................... .............145
ASTERISQUE
359
Let IV be an exceptional spetsial irreducible reflection group acting
on a complex
vedor
space V , i.e.. a group Gn for
я Є
{4,6,8,14,23,24.25.26.27.28.29,30,32,33,34,35.36,37}
in the Shephard-Todd notation. We describe how to deter¬
mine some data associated to the corresponding (split)
spets
G-(ľ.
ІГ),
given complete knowledge of the same data for all
proper subspetses (the method is thus inductive»).
The data determined here are the set Ueh(G) of unipotent
characters of
G
and its repartition into families, as well as the
associated set of Frobenius eigenvalues. The determination of the
Fourier matrices linking unipotent characters and (impotent char¬
acter sheaves will be given in another paper.
The approach works for all split reflection cosets for
primitivt1
irreducible reflection groups. The result is that all the above data
exist and are unique (note that the cuspidal uuipotont degrees are
only determined up to sign).
We keep track of the complete list of axioms used. In order to
do that, we explain in detail some general axioms of spetses . gen¬
eralizing (and sometimes correcting) our paper Toward Spetses
.
Transformation groups
4 (1999).
along the way.
Note that to make the induction work, we must consider a class
of reflection cosets slightly more general than the split, irreducible
ones; the reflection cosets with split semi-simple part, i.e., cosets
(V, W V) such that V
=
£
Y2 with
W
С С1( )
and
φ,
- Id.
We need also to consider some non-exceptional cosets. those asso¬
ciated to
imprimitive
complex reflection groups which appear as
parabolic subgroups of the exceptional ones.
|
| any_adam_object | 1 |
| author | Broué, Michel 1946- Malle, Gunter 1960- Michel, Jean ca. 20./21. Jh |
| author_GND | (DE-588)113828853 (DE-588)1016705093 (DE-588)1050184939 |
| author_facet | Broué, Michel 1946- Malle, Gunter 1960- Michel, Jean ca. 20./21. Jh |
| author_role | aut aut aut |
| author_sort | Broué, Michel 1946- |
| author_variant | m b mb g m gm j m jm |
| building | Verbundindex |
| bvnumber | BV041773629 |
| classification_rvk | SI 832 |
| ctrlnum | (OCoLC)878017941 (DE-599)BVBBV041773629 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV041773629 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T16:54:45Z |
| institution | BVB |
| isbn | 9782856297810 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027219559 |
| oclc_num | 878017941 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-824 DE-384 DE-19 DE-BY-UBM DE-83 DE-29T |
| owner_facet | DE-355 DE-BY-UBR DE-824 DE-384 DE-19 DE-BY-UBM DE-83 DE-29T |
| physical | VI, 146 S. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Soc. Math. de France |
| record_format | marc |
| series | Astérisque |
| series2 | Astérisque |
| spellingShingle | Broué, Michel 1946- Malle, Gunter 1960- Michel, Jean ca. 20./21. Jh Split spetses for primitive reflection groups Astérisque |
| title | Split spetses for primitive reflection groups |
| title_auth | Split spetses for primitive reflection groups |
| title_exact_search | Split spetses for primitive reflection groups |
| title_full | Split spetses for primitive reflection groups Michel Broué ; Gunter Malle ; Jean Michel |
| title_fullStr | Split spetses for primitive reflection groups Michel Broué ; Gunter Malle ; Jean Michel |
| title_full_unstemmed | Split spetses for primitive reflection groups Michel Broué ; Gunter Malle ; Jean Michel |
| title_short | Split spetses for primitive reflection groups |
| title_sort | split spetses for primitive reflection groups |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027219559&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027219559&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV002579439 |
| work_keys_str_mv | AT brouemichel splitspetsesforprimitivereflectiongroups AT mallegunter splitspetsesforprimitivereflectiongroups AT micheljean splitspetsesforprimitivereflectiongroups |