Super-characters of finite unipotent groups of types B n , C n and D n

We define and study super-characters (over the complex field) of the classical finite unipotent groups of types B n , C n and D n . Under the assumption that the prime is sufficiently large, we extend the known results for the unitriangular group proved by the first author in the papers: [C.A.M. And...

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Bibliographic Details
Published inJournal of algebra Vol. 305; no. 1; pp. 394 - 429
Main Authors André, Carlos A.M., Neto, Ana Margarida
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.11.2006
Subjects
Basic set of positive roots
Finite unipotent group
Irreducible character
Orthogonal group
Positive root
Super-character
Symplectic group
Super-character
Irreducible character
Orthogonal group
Positive root
Finite unipotent group
Symplectic group
Basic set of positive roots
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Summary:We define and study super-characters (over the complex field) of the classical finite unipotent groups of types B n , C n and D n . Under the assumption that the prime is sufficiently large, we extend the known results for the unitriangular group proved by the first author in the papers: [C.A.M. André, Basic characters of the unitriangular group, J. Algebra 175 (1995) 287–319], and [C.A.M. André, Basic characters of the unitriangular group (for arbitrary primes), Proc. Amer. Math. Soc. 130 (7) (2002) 1943–1954]. In particular, we prove that every irreducible (complex) character occurs as a constituent of a unique super-character. We also give a combinatorial description of all the irreducible characters of maximum degree.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2006.04.030