Hecke algebras for the basic characters of the unitriangular group

Author:
Carlos A. M. André

Journal:
Proc. Amer. Math. Soc. **132** (2004), 987-996

MSC (2000):
Primary 20C15; Secondary 20G40

DOI:
https://doi.org/10.1090/S0002-9939-03-07143-0

Published electronically:
July 17, 2003

MathSciNet review:
2045413

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Abstract | References | Similar Articles | Additional Information

Abstract: Let denote the unitriangular group of degree over the finite field with elements. In a previous paper we obtained a decomposition of the regular character of as an orthogonal sum of basic characters. In this paper, we study the irreducible constituents of an arbitrary basic character of . We prove that is induced from a linear character of an algebra subgroup of , and we use the Hecke algebra associated with this linear character to describe the irreducible constituents of as characters induced from an algebra subgroup of . Finally, we identify a special irreducible constituent of , which is also induced from a linear character of an algebra subgroup. In particular, we extend a previous result (proved under the assumption where is the characteristic of the field) that gives a necessary and sufficient condition for to have a unique irreducible constituent.

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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/S0002-9939-03-07143-0

Keywords:
Unitriangular group,
irreducible character,
basic character

Received by editor(s):
September 26, 2002

Received by editor(s) in revised form:
December 3, 2002

Published electronically:
July 17, 2003

Communicated by:
Stephen D. Smith

Article copyright:
© Copyright 2003
American Mathematical Society