Welcome to the home page of François Digne


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Position: Emeritus professor at the Université de Picardie Jules-Verne.

Member of the Laboratoire Amiénois de Mathématique Fondamentale et Appliquée ( LAMFA, CNRS, UMR 7352)
Address:
Université de Picardie Jules-Verne
Département de Mathématiques
UFR Sciences
33 Rue Saint-Leu
F-80039 Amiens Cedex 01
France
Phone number: (33) 3 22 82 75 13
Office C005
e-mail : digne@ u-picardie.fr

Mathematical interests

Algebraic groups, particularly over fields of positive characteristic; representations of finite groups of Lie type.

Reflection groups, Hecke algebras, braid and Artin-Tits groups

Some publications and preprints

Braid groups and symplectic Steinberg groups with C. Kassel. (Algebraic K-Theory 8 (2023) 669--692)

Ribbons in Garside monoids with J. Michel.

Formulae for two-variable Green functions (J. Alg. 610 (2022) 270--280) with J. Michel.

Commutation of Shintani descent and Jordan decomposition with J. Michel.

Representations of finite groups of Lie type, 2nd edition, London mathematical society student texts no. 95 (2020) with J. Michel.

Quasi-semisimple elements (Proc. LMS 116, 2018, pp. 1301--1328) with J. Michel.

Dual braid monoids, Mikado braids and positivity in Hecke algebras (Math. Zeit.285, 2017, pp. 215--238) with T. Gobet

Complements on disconnected reductive groups (Pacific J. Math., 279, 2015, pp. 203--228) with J. Michel.

Foundations of Garside Theory (EMS Tracts in Mathematics, vol. 22, 2015), with Patrick Dehornoy, Eddy Godelle, Daan Krammer et Jean Michel . Winner of the "EMS Monograph Award" 2014.

Parabolic Deligne-Lusztig varieties (Advances in Math. 257, 2014, pp. 136--218) with Jean Michel

On character sheaves and characters of reductive groups at unipotent classes (Pure and Applied Math. Quarterly 10, 2014, pp. 459--512), with G. Lehrer and J. Michel.

Addendum to "On character sheaves and characters of reductive groups at unipotent classes"

Garside families and Garside germs, with Patrick Dehornoy, et Jean Michel (Journal of Algebra, Volume 380, 2013, pp. 109--145).

A Garside presentation for Artin-Tits groups of type C̃n (Annales de l'Institut Fourier, tome 62, 2012, pp. 641--666)

The center of pure complex braid groups (Journal of Algebra, Volume 347, 2011, pp. 206--213), with Ivan Marin and Jean Michel

Errata et addenda to F. Digne and J.Michel Representations of finite groups of Lie type London mathematical society student texts no. 21 (1991) (pdf)

From Broué's conjectures to questions in braid group theory (pdf) Conference in Canberra (july 2007)

Garside and locally Garside categories, with J. Michel (arXiv: math.GR/0612652, 2007)

Endomorphisms of Deligne-Lusztig varieties (math.RT/0509011, Nagoya Math. Journal 183, 2006, pp. 35--103), with J. Michel.

Erratum to Endomorphisms of Deligne-Lusztig varieties

Cohomologie des variétés de Deligne-Lusztig (math.RT/0410454, Advances in Math. 209, 2007 pp 749--822) with J. Michel and R. Rouquier.

Présentations duales pour les groupes de tresses de type affine à (math.GR/0402116, Commentarii 86 No 1, 2006 pp 23--47).


Some older publications

  • On the linearity of Artin braid groups, (Journal of Algebra 268, No 1, 2003) pp. 39--57. version dvi
  • The space of unipotently supported class functions (with G. Lehrer and J. Michel, Journal of Algebra 260, No 1 (2003). version dvi ou ps
  • Points fixes des automorphismes quasi-semi-simples (with J. Michel), CRAS 334, No 12 (2002). version ps
  • Springer theory in braid groups and the Birman-Ko-Lee monoid (with D. Bessis et J. Michel), Pacific J. Math. 205, No 2 (2002) 287--309. version pdf
  • Presentation of pure braid groups (with Y. Gomi), Journal for Knot Theory and its Ramifications, vol. 10, No 4 (2001). version dvi
  • Présentation des groupes de tresses pures et de certaines de leurs extensions, preprint (1999).
  • F. Digne et J. Michel, ``On Lusztig's parametrization of characters of finite groups of Lie type'', Astérisque 181-182 (1990) 113--156. version dvi ou ps
  • F. Digne et J. Michel, ``Groupes Réductifs Non Connexes'' Ann. École Normale Supérieure, 4ème série, t. 27 (1994) 345--406. version dvi ou ps
  • On Gel'fand-Graev characters of reductive groups with disconnected centre, Journal de Crelle 491 (1997) 131--148 (with G. Lehrer and J. Michel) version dvi ou ps

    • Complete list of publications