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arXiv · 1709.00547

Indecomposable manipulations with simple modules in category O

Kevin Coulembier·Volodymyr Mazorchuk·Xiaoting Zhang
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Abstract

We study the problem of indecomposability of translations of simple modules in the principal block of BGG category $\mathcal{O}$ for $\mathfrak{sl}_n$, as conjectured in \cite{KiM}. We describe some general techniques and prove a few general results which may be applied to study various special cases of this problem. We apply our results to verify indecomposability for $n\leq 6$. We also study the problem of indecomposability of shufflings and twistings of simple modules and obtain some partial results.

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Kevin Coulembier, Volodymyr Mazorchuk, Xiaoting Zhang. 2017-09-02. Indecomposable manipulations with simple modules in category O. https://arxiv.org/abs/1709.00547

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