On the Restrictions of Modular Irreducible Representations of Algebraic Groups of Type An to Naturally Embedded Subgroups of Type A2

Anna A. Osinovskaya

doi:10.1515/jgth.2005.8.1.43

Published by De Gruyter July 27, 2005

On the Restrictions of Modular Irreducible Representations of Algebraic Groups of Type A_n to Naturally Embedded Subgroups of Type A₂

Anna A. Osinovskaya

From the journal Journal of Group Theory

https://doi.org/10.1515/jgth.2005.8.1.43

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Abstract

Restrictions of irreducible p-restricted representations of algebraic groups of type A_n to naturally embedded subgroups of type A₂ are studied. Let n > 2 and ω = Σⁿ_i=1 m_iω_i be the highest weight of the representation considered. The composition factors of such restrictions are determined in the cases where either n > 5 and Σⁿ_i=1 m_i < p, or n > 3 and m_i + m_i₊₁ + m_i₊₂ + m_i₊₃ < p − 2 for odd i with 1 ≤ i ≤

and m_n−j−₃ + m_n−j−₂ + m_n−j−₁ + m_n−j < p − 2 for even j with 0 ≤ j ≤

. For arbitrary p-restricted representations some large composition factors are found.

Published Online: 2005-07-27

Published in Print: 2005-01-01

On the Restrictions of Modular Irreducible Representations of Algebraic Groups of Type A_n to Naturally Embedded Subgroups of Type A₂

Abstract

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