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arXiv · 1710.06890

Small-dimensional representations of algebraic groups of type $A_l$

Álvaro L. Martínez
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Abstract

For $G$ an algebraic group of type $A_l$ over an algebraically closed field of characteristic $p$, we determine all irreducible rational representations of $G$ in defining characteristic with dimensions $\le (l+1)^s$ for $s = 3, 4$, provided that $l > 18$, $l > 35$ respectively. We also give explicit descriptions of the corresponding modules for $s = 3$.

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Álvaro L. Martínez. 2017-10-20. Small-dimensional representations of algebraic groups of type $A_l$. https://arxiv.org/abs/1710.06890

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