The generic character table of a Sylow p-subgroup of a finite Chevalley group of type D₄

References

• An, J., Hiss, G. (2011). Restricting unipotent characters in finite symplectic groups. Commun. Algebra 39(3): 1104–1130.
   Web of Science ®Google Scholar
• André, C. A. M. (2001). The basic character table of the unitriangular group. J. Algebra 241(1):437–471.
   Web of Science ®Google Scholar
• André, C., Neto, A. (2009). A supercharacter theory for the Sylow p-subgroups of the finite symplectic and orthogonal groups. J. Algebra 322:1273–1294.
   Web of Science ®Google Scholar
• Bradley, J. D., Goodwin, S. M. (2014). Conjugacy classes in Sylow p-subgroups of finite Chevalley groups in bad characteristic. Commun. Algebra 42(8):3245–3258.
   Web of Science ®Google Scholar
• Carter, R. W. (1972). Simple Groups of Lie Type. London: A Wiley-Interscience Publication.
   Google Scholar
• Diaconis, P., Isaacs, I. M. (2008). Supercharacters and superclasses for algebra groups. Trans. Amer. Math. Soc. 360(5):2359–2392.
   Web of Science ®Google Scholar
• Digne, F., Michel, J. (1991). Representations of Finite Groups of Lie Type. London Mathematical Society Student Texts, Vol. 21. Cambridge: Cambridge University Press.
   Google Scholar
• Evseev, A. (2011). Reduction for characters of finite algebra groups. J. Algebra 325:321–351.
   Web of Science ®Google Scholar
• The GAP Group, (2008). GAP – Groups, Algorithms, and Programming, Version 4.4.12. Available at: http://www. gap-system.org.
   Google Scholar
• Geck, M., Hiss, G., Lübeck, F., Malle, G., Pfeiffer, G. (1996). CHEVIE A system for computing and processing generic character tables for finite groups of Lie type, Weyl groups and Hecke algebras. Appl. Algebra Eng. Commun. Comput. 7:175–210.
   Web of Science ®Google Scholar
• Goodwin, S. M. (2006). On the conjugacy classes in maximal unipotent subgroups of simple algebraic groups. Transform. Groups 11(1):51–76.
   Web of Science ®Google Scholar
• Goodwin, S. M., Mosch, P., Röhrle, G. (2014). Calculating conjugacy classes in Sylow p-subgroups of finite Chevalley groups of rank six and seven. LMS J. Comput. Math. 17(1):109–122.
   Web of Science ®Google Scholar
• Goodwin, S. M., Mosch, P., Röhrle, G. (2016). On the coadjoint orbits of maximal unipotent subgroups of reductive groups. Transform. Groups 21(2):399–426.
   Web of Science ®Google Scholar
• Goodwin, S. M., Röhrle, G. (2009). Calculating conjugacy classes in Sylow p-subgroups of finite Chevalley groups. J. Algebra 321:3321–3334.
   Web of Science ®Google Scholar
• Gow, R., Marjoram, M., Previtali, A. (2001). On the irreducible characters of a Sylow 2-subgroup of the finite symplectic group in characteristic 2. J. Algebra 241:393–409.
   Web of Science ®Google Scholar
• Higman, G. (1960). Enumerating p-groups. I: Inequalities. Proc. London Math. Soc. 10:24–30.
   Google Scholar
• Himstedt, F. (2004). Character tables of parabolic subgroups of Steinberg’s triality groups. J. Algebra 281:774–822.
   Web of Science ®Google Scholar
• Himstedt, F. (2007). On the 2-decomposition numbers of Steinberg’s triality groups 3D4(q), q odd. J. Algebra 309: 569–593.
   Web of Science ®Google Scholar
• Himstedt, F. (2007). Character tables of parabolic subgroups of Steinberg’s triality groups 3D4(2n). J. Algebra 316: 254–283.
   Web of Science ®Google Scholar
• Himstedt, F. (2011). On the decomposition numbers of the Ree groups 2F4(q2) in non-defining characteristic. J. Algebra 325:364–403.
   Web of Science ®Google Scholar
• Himstedt, F., Huang, S. (2009). Character table of a Borel subgroup of the Ree groups 2F4(q2). LMS J. Comput. Math. 12:1–53.
   Web of Science ®Google Scholar
• Himstedt, F., Huang, S. (2010). Character tables of the maximal parabolic subgroups of the Ree groups 2F4(q2). LMS J. Comput. Math. 13:90–110.
   Web of Science ®Google Scholar
• Himstedt, F., Huang, S. (2013). On the decomposition numbers of Steinberg’s triality groups 3D4(2n) in odd characteristics. Commun. Algebra 41(4):1484–1498.
   Web of Science ®Google Scholar
• Himstedt, F., Le, T., Magaard, K. (2011). Characters of the Sylow p-subgroups of the Chevalley groups D4(pn). J. Algebra 332:414–427.
   Web of Science ®Google Scholar
• Himstedt, F., Noeske, F. (2014). Decomposition numbers of SO7(q) and Sp6(q). J. Algebra 413:15–40.
   Web of Science ®Google Scholar
• Himstedt, F., Noeske, F. (2015). Restricting unipotent characters in special orthogonal groups. LMS J. Comput. Math. 18:456–488.
   Web of Science ®Google Scholar
• Isaacs, I. M. (1995). Characters of groups associated with finite algebras. J. Algebra 177:708–730.
   Web of Science ®Google Scholar
• Isaacs, I. M. (2007). Counting characters of upper triangular groups. J. Algebra 315(2):698–719.
   Web of Science ®Google Scholar
• Iwaniec, H., Kowalski, E. (2004). Analytic Number Theory. American Mathematical Society Colloquium Publications, Vol. 53. Providence, RI: American Mathematical Society.
   Google Scholar
• Le, T., Magaard, K. (2015). On the character degrees of Sylow p-subgroups of Chevalley groups G(pf) of type E. Forum Math. 27(1):1–55.
   Web of Science ®Google Scholar
• Lehrer, G. (1974). Discrete series and the unipotent subgroup. Compos. Math. 28:9–19.
   Web of Science ®Google Scholar
• Marberg, E. (2011). Combinatorial methods for character enumeration for the unitriangular groups. J. Algebra 345:295–323.
   Web of Science ®Google Scholar
• Marjoram, M. (1999). Irreducible characters of a Sylow p-subgroup of the orthogonal group. Commun. Algebra 27:1171–1195.
   Web of Science ®Google Scholar
• Okuyama, T., Waki, K. (1998). Decomposition numbers of Sp(4,q). J. Algebra 199:544–555.
   Web of Science ®Google Scholar
• Pak, I., Soffer, A. On Higman’s k(Un(𝔽q)) conjecture. Preprint, arxiv:1507.00411.
   Google Scholar
• Previtali, A. (1995). On a conjecture concerning character degrees of some p-groups. Arch. Math. 65:375–378.
   Web of Science ®Google Scholar
• Sangroniz, J. (2003). Character degrees of the Sylow p-subgroups of classical groups. In: Groups St. Andrews 2001 in Oxford, Vol. II. London Math. Soc. Lecture Note Ser., Vol. 305. Cambridge: Cambridge Univ. Press, pp. 487–493.
   Google Scholar
• Sangroniz, J. (2009). Irreducible characters of large degree of Sylow p-subgroups of classical groups. J. Algebra 321:1480–1496.
   Web of Science ®Google Scholar
• Szechtman, F. (2006). Irreducible characters of Sylow subgroups of symplectic and unitary groups. J. Algebra 303: 722–730.
   Web of Science ®Google Scholar
• Szegedy, B. (2003). Characters of the Borel and Sylow subgroups of classical groups. J. Algebra 267:130–136.
   Web of Science ®Google Scholar
• Waki, K. (2004). A note on decomposition numbers of G2(2n). J. Algebra 274:602–606.
   Web of Science ®Google Scholar