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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Minimal polynomials of elements of order $p$ in $p$-modular projective representations of alternating groups


Authors: A. S. Kleshchev and A. E. Zalesski
Journal: Proc. Amer. Math. Soc. 132 (2004), 1605-1612
MSC (2000): Primary 20C30; Secondary 20C20, 20D06
Published electronically: October 21, 2003
MathSciNet review: 2051120
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Abstract: Let $F$ be an algebraically closed field of characteristic $p>0$ and let $G$ be a quasi-simple group with $G/Z(G)\cong A_n$. We describe the minimal polynomials of elements of order $p$ in irreducible representations of $G$ over $F$. If $p=2$, we determine the minimal polynomials of elements of order $4$ in $2$-modular irreducible representations of $A_{n}$, $S_n$, $3\cdot A_6$, $3\cdot S_6$, $3\cdot A_7$, and $3\cdot S_7$.


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Additional Information

A. S. Kleshchev
Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
Email: klesh@math.uoregon.edu

A. E. Zalesski
Affiliation: School of Mathematics, University of East Anglia, Norwich NR4 7TJ, England
Email: a.zalesskii@uea.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07242-3
PII: S 0002-9939(03)07242-3
Received by editor(s): November 18, 2002
Received by editor(s) in revised form: February 19, 2003
Published electronically: October 21, 2003
Communicated by: Stephen D. Smith
Article copyright: © Copyright 2003 American Mathematical Society