Journal of the Ramanujan Mathematical Society

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Reducing the Minimal Representation Modulo 𝓁;An Exercise


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1 Department of Mathematics, University of Utah, Salt Lake City, UT 84112, United States
     

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Let G be a simply connected Chevalley group over a p-adic field, with the residue field of order q, corresponding to an irreducible simply laced ischolar_main system. We show that the minimal representation V of G can be defined over ℚ. We show that the reduction of V modulo 𝓁≠p is minimal (in appropriate sense) and is irreducible for 𝓁 outside an explicit, finite set determined by q.
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  • Reducing the Minimal Representation Modulo 𝓁;An Exercise

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Authors

Gordan Savin
Department of Mathematics, University of Utah, Salt Lake City, UT 84112, United States

Abstract


Let G be a simply connected Chevalley group over a p-adic field, with the residue field of order q, corresponding to an irreducible simply laced ischolar_main system. We show that the minimal representation V of G can be defined over ℚ. We show that the reduction of V modulo 𝓁≠p is minimal (in appropriate sense) and is irreducible for 𝓁 outside an explicit, finite set determined by q.