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August 10, 2017


List of Publications of Gerhard Hiss


(A) Articles in refereed journals

  1. (with K. Magaard)   Imprimitive irreducible modules for finite quasisimple groups, II, Trans. Amer. Math. Soc., to appear.
  2. (with T. Gerber)   Branching graphs for finite unitary groups in non-defining characteristic, Comm. Algebra 45 (2017), 561-574.
  3. (with T. Gerber and N. Jacon)   Harish-Chandra series in finite unitary groups and crystal graphs, Int. Math. Res. Not. 2015, No. 22 (2015), 12206-12250. DOI: 10.1093/imrn/rnv058, Advance Access published March 9, 2015.
  4. (with W. J. Husen and K. Magaard)   Imprimitive irreducible modules for finite quasisimple groups, Mem. Amer. Math. Soc., Volume 234, Number 1104, 2015, ISBN: 978-1-4704-0960-9 (print), DOI: http://dx.doi.org/10.1090/memo/1104, Published electronically: August 1, 2014.
  5. (with J. Müller, F. Noeske and J. Thackray)  The Brauer characters of the sporadic simple Harada-Norton group and its automorphism group in characteristics 2 and 3, LMS J. Comput. Math. 15 (2012), 257-280.
  6. (with N. Naehrig)  The Classification of the Indecomposable Liftable Modules in Blocks with Cyclic Defect Groups, Bull. Lond. Math. Soc. 44 (2012), 974-980.
  7. (with S. Koenig and N. Naehrig) On the socle of an endomorphism algebra, J. Pure Appl. Algebra 216 (2012), 1288-1294.
  8. (with H.-X. Chen) Notes on the Drinfeld double of finite-dimensional group algebras, Algebra Colloq. 19 (2012), 483-492.
  9. (with A. Zalesski) Corrigendum to "The Weil-Steinberg character of finite classical groups", Represent. Theory 15 (2011), 729-732.
  10. (with A. Szczepanski)  Corrigendum to: Spin structures on flat manifolds with cyclic holonomy, Comm. Algebra 39 (2011), 2659.
  11. (with J. An) Restricting Unipotent Characters in Finite Symplectic Groups, Comm. Algebra 39 (2011), 1104 -1130.
  12. Principal blocks and the Steinberg character, Algebra Colloq. 17 (2010), 361 - 364.
  13. (with A. Zalesski) Tensoring Generalized Characters with the Steinberg Character, Proc. Amer. Math. Soc. 138 (2010), 1907 - 1921.
  14. (with A. Zalesski, appendix by O. Brunat) The Weil-Steinberg character of finite classical groups, Represent. Theory 13 (2009), 427 - 459. Corrigendum
  15. (with A. Szczepanski)  Spin structures on flat manifolds with cyclic holonomy, Comm. Algebra 36 (2008), 11 - 22. Corrigendum
  16. (with J. An)  Restricting the Steinberg character in finite symplectic groups, J. Group Theory 9 (2006), 251 - 264.
  17. (with M. Neunhöffer and F. Noeske) The 2-modular characters of the Fischer group Fi23, J. Algebra 300 (2006), 555 - 570.
  18. (with R. Kessar)  Scopes reduction and Morita equivalence classes of blocks in finite classical groups II, J. Algebra 283 (2005), 522 - 563.
  19. (with H.-X. Chen) Projective summands in tensor products of simple modules of finite dimensional Hopf algebras, Comm. Algebra 32 (2004), 4247 - 4264.
  20. Hermitian function fields, classical unitals, and representations of 3-dimensional unitary groups, Indag. Math. (N.S.) 15 (2004), 223-243.

  21. Die sporadischen Gruppen, Jahresber. Deutsch. Math.-Verein. 105 (2003), 169-194.

  22. (with G. Malle)  Low-dimensional representations of quasi-simple groups, LMS J. Comput. Math. 4 (2001), 22-63. Corrigenda, LMS J. Comput. Math. 5 (2002), 95-126.

  23. (with G. Malle)  Low-dimensional representations of special unitary groups, J. Algebra 236 (2001), 745-767.

  24. (with R. Kessar)  Scopes reduction and Morita equivalence classes of blocks in finite classical groups, J. Algebra 230 (2000), 378-423.

  25. (with A. Henke and J. Müller)  The 7-modular decomposition matrices of the sporadic O'Nan group, J. London Math. Soc. 60 (1999), 58-70.

  26. (with F. Lübeck)  The Brauer trees of the exceptional Chevalley groups of types F4 and  2E6, Arch. Math. 70 (1998), 16-21.

  27. (with Gene Cooperman, Klaus Lux, and Jürgen Müller)   The Brauer tree of the principal 19-block of the sporadic simple Thompson group, Exp. Math. 6 (1997), 293-300.

  28. (with A. Szczepanski)  Flat manifolds with only finitely many affinities, Bull. Polish Acad. Sci. Math. 45 (1997), 349-357.

  29. Decomposition matrices of the Chevalley group F4(2) and its covering group, Comm. Algebra 25 (1997), 2539-2555.

  30. (with J. Gruber)  Decomposition numbers of finite classical groups for linear primes, J. reine angew. Math. 485 (1997), 55-91.

  31. On the incidence matrix of the Ree unital, Des. Codes Cryptogr. 10 (1997), 57-62.

  32. Supercuspidal representations of finite reductive groups, J. Algebra 184 (1996), 839-851.

  33. (with M. Geck, F. Lübeck, G. Malle, and G. Pfeiffer)   CHEVIE-A system for computing and processing generic character tables, AAECC 7 (1996), 175-210.

  34. (with M. Geck and G. Malle)  Towards a classification of the irreducible representations in non-defining characteristic of a finite group of Lie type, Math. Z. 221 (1996), 353-386.

  35. (with K. Lux and J. Müller)  The 2-modular decomposition matrices of the non-principal blocks of maximal defect of the triple cover of the sporadic simple McLaughlin group, J. Symb. Comp. 19 (1995), 585-600.

  36. (with F. Bleher and W. Kimmerle), Autoequivalences of blocks and a conjecture of Zassenhaus, J. Pure Appl. Algebra 103 (1995), 23-43.

  37. (with J. Müller)  The 5-modular characters of the sporadic simple Rudvalis group and its covering group, Comm. Algebra 23 (1995), 4633-4667.

  38. (with A. Szczepanski)  Holonomy groups of Bieberbach groups with finite outer automorphism groups, Arch. Math. 65 (1995), 8-14.

  39. (with F. Lübeck and G. Malle)  The Brauer trees of the exceptional Chevalley groups of type E6, Manuscripta Math. 87 (1995), 131-144.

  40. (with M. Geck and G. Malle)  Cuspidal unipotent Brauer characters, J. Algebra 168 (1994), 182-220.

  41. (with D. L. White)  The 5-modular characters of the covering group of the sporadic simple Fischer group Fi22 and its automorphism group, Comm. Algebra 22 (1994), 3591-3611.

  42. (with K. Lux, appendix by T. Breuer)   The 5-modular characters of the sporadic simple Fischer groups Fi22 and Fi23, Comm. Algebra 22 (1994), 3563-3590.

  43. The 3-modular characters of the Rudvalis group and its covering group, Math. Comput. 62 (1994), 851-863.

  44. Harish-Chandra series of Brauer characters in a finite group with a split BN-pair, J. London Math. Soc. 48 (1993), 219-228.

  45. (with J. Shamash)  2-Blocks and 2-decomposition numbers of the Chevalley groups G2(q), Math. Comput., 59 (1992), 645-672.

  46. (with K. Lux and R. Parker)  The 5-modular characters of the McLaughlin group and its covering group, Manuscripta Math., 73 (1991), 91-114.

  47. (with M. Geck)  Basic sets of Brauer characters of finite groups of Lie type, J. reine angew. Math., 418 (1991), 173-188.

  48. The Brauer trees of the Ree groups, Comm. Algebra, 19 (1991), 871-888.

  49. (with A. Szczepanski)  On torsion free crystallographic groups, J. Pure Appl. Algebra, 74 (1991), 39-56.

  50. (with J. Shamash)  3-Blocks and 3-decomposition numbers of G2(q), J. Algebra, 131 (1990), 371-387.

  51. Regular and semisimple blocks of finite reductive groups, J. London Math. Soc., 41 (1990), 63-68.

  52. The number of trivial composition factors of the Steinberg module, Arch. Math., 54 (1990), 247-251.

  53. On the decomposition numbers of G2(q), J. Algebra, 120 (1989), 339-360.

  54. (with K. Lux)  The Brauer characters of the Hall-Janko group, Comm. Algebra, 16 (1988), 357-398.

  55. A converse to the Fong-Swan-Isaacs theorem, J. Algebra, 111 (1987), 279-290.

  56. The modular characters of the Tits simple group and its automorphism group, Comm. Algebra, 14 (1986), 125-154.

  57. (with K. Lux)  On the decomposition matrices of twisted group algebras, Comm. Algebra, 13 (1985), 2219-2229.

  58. Groups whose Brauer-characters are liftable, J. Algebra, 94 (1985), 388-405.

  59. Die adjungierten Darstellungen der Chevalley-Gruppen, Arch. Math., 42 (1984), 408-416.

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(B) Articles in books (*: refereed article)

  1. (with F. Lübeck)   Some remarks on two-transitive permutation groups as multiplication groups of quasigroups*, in: N. S. Narasimha Sastry (Ed.), Buildings, Finite Geometries and Groups, Springer, 2011, pp. 81-91.
  2. Finite groups of Lie type and their representations*, in: C. M. Campbell, M. R. Quick, E. F. Robertson, C. M. Roney-Dougal, G. C. Smith and G. Traustason (Eds.), Groups St Andrews 2009 in Bath, Cambridge University Press, Cambridge, 2011, pp. 1-40.
  3. (with F. Lübeck)  Some observations on products of characters of finite classical groups*, in: C. Y. Ho, P. Sin, P. H. Tiep, and A. Turull (Eds.), Finite Groups 2003, Proceedings of the Gainesville Conference on Finite Groups, March 6-12, 2003, de Gruyter, 2004, pp. 195-207.
  4. Algorithms of representation theory, in: J. Grabmeier, E. Kaltofen, and V. Weispfenning (Eds.): Computer Algebra Handbook, Springer-Verlag, Berlin Heidelberg, 2003, Section 2.8, pp. 84-88.

  5. Computer algebra in group theory, in: J. Grabmeier, E. Kaltofen, and V. Weispfenning (Eds.): Computer Algebra Handbook, Springer-Verlag, Berlin Heidelberg, 2003, Subsection 3.2.1, pp. 196-197.

  6. (with K. Lux)  MOC, in: J. Grabmeier, E. Kaltofen, and V. Weispfenning (Eds.): Computer Algebra Handbook, Springer-Verlag, Berlin Heidelberg, 2003, Subsection 4.2.28, pp. 429-430.

  7. Morita equivalences between blocks of finite Chevalley groups, in: N. Kawanaka, G. Michler, and K. Uno (Eds.): The Proceedings of ''Representation Theory of Finite and Algebraic Groups'', Osaka University, Osaka, 2000, pp. 128-136.

  8. On a question of Brauer in modular representation theory of finite groups, in: S. Koshitani (Ed.): Representation Theory of Finite Groups and Related Topics, RIMS Kokyuroku 1149, Kyoto University, Kyoto, 2000, pp. 21-29.

  9. (with R. Dipper, M. Geck, and G. Malle)   Representations of Hecke algebras and finite groups of Lie type*, in: B. H. Matzat, G.-M. Greuel, and G. Hiss (Eds.): Algorithmic Algebra and Number Theory, Springer-Verlag, Heidelberg, 1999, pp. 331-378.

  10. Harish-Chandra theory, q-Schur algebras, and decomposition matrices for finite classical groups*, in: R. Curtis and R. Wilson (Eds.): The Atlas of Finite Groups: Ten Years On, Cambridge University Press, 1998, pp. 58-73.

  11. (with M. Geck)  Modular representations of finite groups of Lie type in non-defining characteristic*, in: M. Cabanes (Ed.): Finite reductive groups: Related structures and representations, Birkhäuser, 1997, pp. 195-249.

  12. Zur Donovan Vermutung, in: B. Külshammer and K. Rosenbaum (Eds.): Darstellungstheorietage Jena 1996, Akademie gemeinnütziger Wissenschaften zu Erfurt, Mathematisch-Naturwissenschaftliche Klasse, Sitzungsberichte 7 (1996), pp. 67-73.

  13. Decomposition numbers of finite groups of Lie type in non-defining characteristic*, in G.O. Michler and C.M. Ringel (Eds.): Representation Theory of Finite Groups and Finite-Dimensional Algebras, Birkhäuser 1991, pp. 405-418.

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(C) Preprints

  1. (with N. Naehrig)   The Indecomposable Liftable Modules in Cyclic Blocks, unpublished preprint, 2010.
  2. A note on the Chevalley property of finite group algebras, unpublished preprint, 2004.

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(D) Monograph

  1. (with K. Lux) Brauer Trees of Sporadic Groups, 526 pages, Oxford University Press, 1989.

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(E) Editions

  1. (with B. H. Matzat and G.-M. Greuel)   Algorithmic Algebra and Number Theory, Springer-Verlag, Heidelberg, 1999.

  2. (with M. Bhargava, R. Guralnick, K. Lux and P. H. Tiep)   Finite Simple Groups: Thirty Years of the Atlas and Beyond, Contemporary Mathematics Vol. 694, AMS, 2017.

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(F) Computer algebra systems

  1. (with C. Jansen, K. Lux, and R. Parker) MOC-A Program System for Handling Brauer Characters, unpublished.

    Description in: G. Hiss, C. Jansen, K. Lux, and R. Parker, Computational modular character theory, 1993.

  2. (with M. Geck, F. Lübeck, G. Malle, and G.  Pfeiffer) CHEVIE-A computer algebra system for computing and processing generic character tables of finite groups of Lie type, Hecke algebras and Weyl groups, first released 29.10.1993.

    Description and manual in: M. Geck, G Hiss, F. Lübeck, G. Malle, and G.  Pfeiffer,   CHEVIE-Generic character tables of finite groups of Lie type, Hecke algebras and Weyl groups, IWR-Preprint 93 - 62, Interdisziplinäres Zentrums für Wissenschaftliches Rechnen, Universität Heidelberg, Heidelberg, 1993.


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(G) Theses

  1. Zerlegungszahlen endlicher Gruppen vom Lie-Typ in nicht-definierender Charakteristik, Habilitationsschrift, Aachen 1990.

  2. Über Liftbarkeit modularer Darstellungen endlicher Gruppen, Dissertation, Freiburg 1983.

  3. Beschreibung endlicher Gruppen durch die Grade ihrer irreduziblen Charaktere, Diplomarbeit, Freiburg 1981.

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