Welcome on Jean Michel's home page
Position: Director of research emeritus (CNRS)
Work Address
UFR de Mathématiques,
Université de Paris cité (Denis Diderot - Paris 7)
Bat. Sophie Germain Case 7012,
75205 Paris Cedex 13 France
Email: jean.michel@imj-prg.fr
Office: room 639
Phone: (33) 0157279144
Administrative links
Project Groupes, Représentations et Géométrie
UMR 7586 (Mathématiques)
UFR de Mathématiques
(Université Paris 7)
My research interests
My original research area is reductive algebraic groups and finite
groups of Lie type (the points over a finite field), and their
representations in non-defining characteristic; my interests extend to
related domains, such as rational, real or complex (pseudo-)reflection
groups, Hecke (and cyclotomic Hecke) algebras and associated braid groups.
In particular, I have studied Alvis-Curtis duality, Shintani descent, the
Weil representation, Gelfand-Graev representations, disconnected reductive
groups, blocks with abelian defect group of finite reductive groups,
Deligne-Lusztig varieties, Spetses.
I have written packages for computing in the
above mentioned domains, in particular I am an author of the Chevie and VKcurve GAP3 packages, and the
Julia package
Gapjm.
Preprints
François Digne and Jean Michel
Ribbons in Garside monoids.
math.GR/2206.00548
François Digne and Jean Michel
Garside and locally Garside categories.
math.GR/0612652
Some publications
Jean Michel
Tower equivalence and Lusztig's truncated Fourier transform.
math.RT/2207.08462
Proc. AMS series B vol. 10 (2023) 252--261
François Digne and Jean Michel
Formulae for two-variable Green functions.
math.RT/2102.04055
J. Algebra. 610 (2022) 270--280
François Digne and Jean Michel
Commutation of Shintani descent and Jordan decomposition.
math.RT/2007.08819
Indag. Math. 32 (2021) 1229--1239
Errata to F. Digne and J.Michel Representations of finite groups
of Lie type London mathematical society student texts no. 95 (2020).
pdf
François Digne and Jean Michel
Quasi-semisimple elements.
math.GR/1707.01328
Proceeding of the London mathematical society 116 (2018) 1301--1328
Michel Broué, Ruth Corran and Jean Michel
Cyclotomic root systems and bad primes.
Advances in Math. 325 (2018) 375--458
Michel Enguehard and Jean Michel
The Sylow subgroups of a finite reductive group.
math.GR/1602.01424
Bull. of the institute of Math. Academia Sinica 13 (2018) 227--247
Jean Michel
"Case-free" derivation for Weyl groups of the number of reflection
factorizations of a Coxeter element.
arXiv:1408.0721 [math.RT]
Proceedings of AMS 144 (2016) 937--941
François Digne and Jean Michel
Complements on disconnected reductive groups.
arXiv:1502.06751 [math.RT]
Pacific J. of math. 279 (2015) 203--228
Patrick Dehornoy, with François Digne,
Eddy Godelle, Daan Krammer, Jean Michel
Foundations of Garside Theory
Version du 22 Décembre 2014
EMS tracts in mathematics no. 22 (2015) 1--691.
Jean Michel
The development version of the CHEVIE package of GAP3.
arXiv:1310.7905 [math.RT]
J. of Algebra 435 (2015) 308--336
François Digne and Jean Michel
Parabolic Deligne-Lusztig varieties.
arXiv:1110.4863v1 [math.GR]
Advances in Math. 257 (2014) 136--218
Michel Broué, Gunter Malle and Jean Michel
Split Spetses for primitive reflection groups.
arXiv:1204.5846v1 [math.GR]
Astérisque 359 (2014) 1--146
François Digne, Gus Lehrer and Jean Michel
On character sheaves and characters of reductive groups at unipotent
classes.
arXiv:1307.0698 [math.RT]
Pure and Applied Math. Quarterly 10 (2014) 459--512
Note: Jay Taylor in “Evaluating characteristic functions of
character sheaves at unipotent elements”, Repr. Theory 18 (2014),
310--340, Theorem 7.7, has independently obtained our Theorem 4.1(ii)
by completely different methods.
Patrick Dehornoy, François Digne and Jean Michel
Garside families and Garside germs.
arXiv:1208.3362 [math.GR]
Journal of Algebra, Volume 380, 15 April 2013, Pages 109-145
C. Bonnafé and J. Michel Computational proof of the Mackey
formula for q>2
math.RT/1003.4922
Journal of algebra. Volume 327, (2011), 506--526
François Digne, Ivan Marin and Jean Michel
The center of pure complex braid groups.
abs/1103.2898
Journal of algebra. Volume 347, Issue 1, 1 December 2011, Pages 206-213
G. Malle and J. Michel Constructing representations of Hecke algebras
for complex reflection groups
LMS J. Comput. Math. 13 (2010) 426--450
math.RT/0909.4040
Erratum
I. Marin and J. Michel Automorphisms of complex reflection groups
math.RT/0701266,
Representation Theory 14 (2010) 747--788
F. Digne, J. Michel et R. Rouquier Cohomologie des
variétés de Deligne-Lusztig
math.RT/0410454
Advances in Math. 209 (2007) 749--822.
C. Bonnafé, G. I. Lehrer and J. Michel Twisted
invariant theory for reflection groups
math.RT/0505087
Nagoya Mathematical Journal 182 (2006) 1--35.
F. Digne and J. Michel Endomorphisms of Deligne-Lusztig varieties
math.RT/0509011
Nagoya Mathematical Journal 183 (2006) 35--103.
Erratum pdf
J. Michel Hurwitz action on tuples of Euclidean reflections
math.AG/0410313
Journal of Algebra 295 (2006) 289--292
D.Bessis and J.Michel Explicit presentations for exceptional braid
group,
math.GR/0312191 .
Experimental mathematics 13 (2004) No. 2 257--266.
F. Digne, G.I. Lehrer and J. Michel On the
space of unipotently supported functions on a finite
reductive group, J. Algebra 260(2003) 111--137
dvi voir aussi math.GR/0206076
.
G.I.Lehrer and J.Michel Invariant theory and eigenspaces for
unitary reflection groups, C.R.A.S., Ser. I 336 (2003) 795--800.
dvi
F. Digne et J. Michel
Fixed points of quasi-semi-simple automorphisms, C.R.A.S.,
Ser. I (334) 2002 p. 1055--1060
dvi
D. Bessis, F. Digne and J. Michel Springer theory in braid groups
and the Birman-Ko-Lee monoid, Pacific Journal of Math., 205 No 2
(2002) 287--309 pdf
J.Michel Calculs en théorie des groupes et introduction
au langage GAP , Journées mathématiques X-UPS
2000, ``groupes finis'', 71--94, Éditions de l'école
Polytechnique dvi
J.Michel A note on words in braid monoids, Journal of
Algebra 215 (1999) 366--377 dvi
M. Broué, G. Malle and J.Michel Towards Spetses I,
Transformation groups 4 (1999) 157--218 dvi
M. Geck et J. Michel ``good'' elements of finite Coxeter groups
and representations of Iwahori--Hecke algebras, Proc. London Math.
Soc. (74) No.3 (1997) 275--305. dvi
F.Digne, G. Lehrer et J.Michel On Gel'fand-Graev characters of
reductive groups with disconnected centre, Journal de Crelle 491
(1997) 131--147. dvi
M. Broué et J. Michel Sur certains éléments
réguliers des groupes de Weyl et les variétés
de Deligne--Lusztig associées, dans Finite Reductive
Groups, Progress in Mathematics No 141, Birkhauser (1996)73--139.
dvi
A.-M. Aubert, J. Michel et R. Rouquier Correspondance de Howe
pour les groupes finis, Duke Math. Journal., vol. 83 No. 2, (1996)
353--397. dvi
F. Digne et J. Michel Groupes Réductifs Non Connexes,
Ann. École Normale Supérieure, 4ième série,
t. 27 (1994) 345--406. dvi
M. Broué, G. Malle et J. Michel Generic Blocks of
Finite Reductive Groups, Astérisque 212 (1993) 7--92. dvi
M. Broué et J. Michel Blocs à groupe de
défaut abélien Astérisque 212 (1993) 93--118,
dvi
F. Digne, G.I. Lehrer et J. Michel The characters of the group of
rational points of a reductive group with non-connected centre,
Journal de Crelle 425 (1992) 155--192. dvi
Errata to F. Digne and J.Michel Representations of finite groups
of Lie type London mathematical society student texts no. 21 (1991).
pdf
F. Digne et J. Michel On Lusztig's parametrization of
characters of finite groups of Lie type, Astérisque
181-182 (1990) 113--156. dvi
F. Digne et J. Michel Lusztig Functor and Shintani
Descent, Rapport de Recherche du L.M.E.N.S. 1989 No. 2 dvi
F. Digne et J. Michel Caractères des groupes
linéaires et unitaires et foncteurs de Lusztig, Journal of
Algebra 107 No 1 (1987) 217--255. dvi
Lecture Notes
"Groupes de tresses, groupes réductifs et algèbres de
Hecke" given spring 1998 (in French, format .pdf)
"Groupes de réflexions complexes" given autumn 2004 (in French, format .pdf)
"Groupes algébriques II" given winter 2014 (in French, format .pdf)
"Lectures on Coxeter groups" given in
Beijing, april--may 2014 (in English, format .pdf)
"Lectures on finite reductive groups and their representations"
lectures shared with Olivier Dudas;
given in Beijing, april--june 2015 (in English, format .pdf)
A table of complex reflection groups
.pdf format,
Tables
Complex reflection groups
Their maximal eigenspaces
Programs
Ready to download GAP3 distribution with the
packages Chevie
and VKcurve.
There is now a Julia version
Gapjm
of these packages.
List of publications
pdf
Some of my hobbies...
The Go game
Rhopalocera