Abelian subgroups and semisimple elements in $2$-modular representations of the symplectic group $Sp_{2n}(2)$

Alexandre Zalesski

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arXiv · 2004.01287

Abelian subgroups and semisimple elements in $2$-modular representations of the symplectic group $Sp_{2n}(2)$

Alexandre Zalesski

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Abstract

We determine the irreducible 2-modular representations of the symplectic group $G=Sp_{2n}(2)$ whose restriction to every abelian subgroup has a trivial constituent. A similar result is obtained for maximal tori of $G$. There is significant information on the existence of eigenvalue 1 of elements of $G$ in a given irreducible representation of $G$.

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BibTeX RIS

Alexandre Zalesski. 2020-04-02. Abelian subgroups and semisimple elements in $2$-modular representations of the symplectic group $Sp_{2n}(2)$. https://arxiv.org/abs/2004.01287

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