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arXiv · 1401.8202

Some Weyl modules of the algebraic groups of type $E_6$

Peter Sin
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Abstract

Let $G$ be a simple algebraic group of type $E_6$ over an algebraically closed field of characteristic $p>0$. We determine the submodule structure of the Weyl modul es with highest weight $r\omega_1$ for $0\leq r\leq p-1$, where $\omega_1$ is the fundamental weight of the standard $27$-dimensional module. In the process, the structures of other Weyl modules with highest weights linked to $r\omega_1$ are also found. %We also give some computations for the Weyl modules with highest weights %of the form $r(\omega_1+\omega_6)$, which arise in the study of %the graph automorphism and associated twisted finite groups.

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Peter Sin. 2014-01-31. Some Weyl modules of the algebraic groups of type $E_6$. https://arxiv.org/abs/1401.8202

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