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 | References | Similar Articles | Additional Information

Abstract: Let denote the (upper) unitriangular group of degree over the finite field with elements. In this paper we consider the basic (complex) characters of and we prove that every irreducible (complex) character of is a constituent of a unique basic character. This result extends a previous result which was proved by the author under the assumption , where is the characteristic of the field .

**1.**C. A. M. André,*Basic characters of the unitriangular group*, J. Algebra**175**(1995), 287-319. MR**96h:20081a****2.**C. A. M. André,*Basic sums of coadjoint orbits of the unitriangular group*, J. Algebra**176**(1995), 959-1000. MR**96h:20081b****3.**C. A. M. André,*The regular character of the unitriangular group*, J. Algebra**201**(1998), 1-52. MR**98k:20071****4.**C. A. M. André,*The basic character table of the unitriangular group*, J. Algebra**241**(2001), 437-471.**5.**C. A. M. André,*Irreducible characters of finite algebra groups*, Proceedings of the Workshop ``Matrices and Group Representations'', p. 65-80, Textos de Matemática, Série B, n. 19, Departamento de Matemática da Universidade de Coimbra, Coimbra, Portugal, 1999. MR**2001g:20009****6.**E. Artin,*Geometric algebra*, Interscience, New York, 1957. MR**18:553e****7.**C. W. Curtis and I. Reiner,*Methods of representation theory (with applications to finite groups and orders, Vol. 1*, Wiley-Interscience, New York, 1981. MR**82i:20001****8.**B. Huppert,*Character theory of finite groups*, Walter de Gruyter, Berlin, 1998. MR**99j:20011****9.**I. M. Isaacs,*Character theory of finite groups*, Dover, New York, 1994. CMP**94:14****10.**I. M. Isaacs,*Characters of groups associated with finite algebras*, J. Algebra**177**(1995), 708-730. MR**96k:20011****11.**I. M. Isaacs and D. Karagueuzian,*Conjugacy in groups of upper triangular matrices*, J. Algebra**202**(1998), 704-711. MR**99b:20011****12.**G. I. Lehrer,*Discrete series and the unipotent subgroup*, Compositio Math.**28**(1974) 9-19. MR**49:5193**

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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