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Basic characters of the unitriangular group (for arbitrary primes)


Author: Carlos A. M. André
Journal: Proc. Amer. Math. Soc. 130 (2002), 1943-1954
MSC (2000): Primary 20C15; Secondary 20G40
DOI: https://doi.org/10.1090/S0002-9939-02-06287-1
Published electronically: January 17, 2002
MathSciNet review: 1896026
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Abstract: Let $U_{n}(q)$ denote the (upper) unitriangular group of degree $n$ over the finite field $\mathbb{F}_{q}$ with $q$ elements. In this paper we consider the basic (complex) characters of $U_{n}(q)$ and we prove that every irreducible (complex) character of $U_{n}(q)$ is a constituent of a unique basic character. This result extends a previous result which was proved by the author under the assumption $p \geq n$, where $p$ is the characteristic of the field $\mathbb{F}_{q}$.


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Additional Information

Carlos A. M. André
Affiliation: Departamento de Matemática e Centro de Estruturas Lineares e Combinatórias, Faculdade de Ciências da Universidade de Lisboa, Rua Ernesto de Vasconcelos, Edifício C1, Piso 3, 1749-016 Lisboa, Portugal
Email: candre@fc.ul.pt

DOI: https://doi.org/10.1090/S0002-9939-02-06287-1
Keywords: Unitriangular group, irreducible character, basic character, coadjoint orbit, basic subvariety
Received by editor(s): July 18, 2000
Received by editor(s) in revised form: February 5, 2001
Published electronically: January 17, 2002
Communicated by: Stephen D. Smith
Article copyright: © Copyright 2002 American Mathematical Society

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