The irreducible characters of the Sylow p-subgroups of the Chevalley groups D6(pf) and E6(pf). (November 2019)

• Record Type: Journal Article
• Authors: Le, Tung; Magaard, Kay; Paolini, Alessandro
• Is Part Of: Journal of symbolic computation. Volume 95(2019)
• Page Start: 68
• Page End: 99
• Publication Date: 2019-11
• Subjects: Irreducible characters -- Sylow subgroups -- Nonabelian cores -- Bad primes; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2019.02.001
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We parametrize the set of irreducible characters of the Sylow p -subgroups of the Chevalley groups D 6 ( q ) and E 6 ( q ), for an arbitrary power q of any prime p . In particular, we establish that the parametrization is uniform for p ≥ 3 in type D 6 and for p ≥ 5 in type E 6, while the prime 2 in type D 6 and the primes 2, 3 in type E 6 yield character degrees of the form q m / p i which force a departure from the generic situations. Also for the first time in our analysis we see a family of irreducible characters of a classical group of degree q m / p i where i > 1 which occurs in type D 6 .