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Supercharacters and pattern subgroups in the upper triangular groups

Part of:Representation theory of groups

Published online by Cambridge University Press:  21 November 2012

Tung Le
Tung Le*
Affiliation:
Faculty of Mathematics and Computer Science, Vietnam National University, Ho Chi Minh City, Vietnam (lttung96@yahoo.com)
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Abstract

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Let Un(q) denote the upper triangular group of degree n over the finite field $\mathbb{F}_q$ with q elements. It is known that irreducible constituents of supercharacters partition the set of all irreducible characters Irr(Un(q)). In this paper we present a correspondence between supercharacters and pattern subgroups of the form Uk(q) ∩ wUk(q), where w is a monomial matrix in GLk(q) for some k < n.

Keywords

root systemirreducible charactertriangular group

MSC classification

Secondary:20C33: Representations of finite groups of Lie type20C15: Ordinary representations and characters

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 56 , Issue 1 , February 2013, pp. 177 - 186
Copyright
Copyright © Edinburgh Mathematical Society 2012

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