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Published June 2015 | Submitted
Journal Article Open

Irreducible adjoint representations in prime power dimensions, with an application

Abstract

We construct an infinite family of representations of finite groups with an irreducible adjoint action and we give an application to the question of lacunary of Frobenius traces in Galois representations.

Additional Information

© 2015 Ramanujan Mathematical Society. Received: July 28, 2014. We would like to thank Dinakar Ramakrishnan for suggesting the problem and for his invaluable help and encouragement. We are grateful to Michael Aschbacher for outlining the construction that appears in Section 4 and also for his useful comments and suggestions. We would like to acknowledge helpful conversations with Iurie Boreico, Hadi Hedayatzadeh and Andrei Jorza.

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