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.


  • 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

  • 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.
  • 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,


    Complex reflection groups
    Their maximal eigenspaces


    Ready to download GAP3 distribution with the packages Chevie and VKcurve. I am working on an port of these packages to Julia.

    List of publications

  • pdf

  • Some of my hobbies...

  • The Go game
  • Rhopalocera