Tensor products of the defining representations over the Witt algebra in positive characteristic

Hao Chang; Yu-Feng Yao

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arXiv · 2108.06657

Tensor products of the defining representations over the Witt algebra in positive characteristic

Hao Chang·Yu-Feng Yao

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Abstract

Let $A(1):=k[X]/(X^p)$ be the natural representation of the Witt algebra $W(1)$ over an algebraically closed field of prime characteristic $p>3$. In this note, we decompose the $W(1)$-module $A(1)\otimes A(1)$ into two invariant subspaces, and precisely construct their Jordan-H\"older composition series. As a consequence, we obtain all decomposition factors of the tensor product of the simple restricted $W(1)$-module with "highest" weight $p-1$.

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BibTeX RIS

Hao Chang, Yu-Feng Yao. 2021-08-15. Tensor products of the defining representations over the Witt algebra in positive characteristic. https://arxiv.org/abs/2108.06657

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