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ASYMPTOTIC BOUNDS FOR THE SIZE OF Hom(A, GLn(q))

Part of: Representation theory of groups Linear algebraic groups and related topics

Published online by Cambridge University Press:  14 March 2017

MICHAEL BATE  and
ALEC GULLON
MICHAEL BATE
Affiliation:
Department of Mathematics, University of York, York YO10 5DD, United Kingdom e-mail: michael.bate@york.ac.uk
ALEC GULLON
Affiliation:
Department of Mathematics, Lancaster University, Lancaster, LA1 4YF, United Kingdom e-mail: a.gullon@lancaster.ac.uk
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Abstract

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Fix an arbitrary finite group A of order a, and let X(n, q) denote the set of homomorphisms from A to the finite general linear group GLn(q). The size of X(n, q) is a polynomial in q. In this note, it is shown that generically this polynomial has degree n2(1 – a−1) − εr and leading coefficient mr, where εr and mr are constants depending only on r := n mod a. We also present an algorithm for explicitly determining these constants.

MSC classification

Primary: 20G40: Linear algebraic groups over finite fields
Secondary: 20C15: Ordinary representations and characters
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 60 , Issue 1 , January 2018 , pp. 51 - 61
Copyright
Copyright © Glasgow Mathematical Journal Trust 2017 

References

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