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arXiv · 2403.15018

Computing monomial bases in Lie theory using OSCAR

Xin Fang·Ghislain Fourier·Lars Göttgens·Ben Wilop
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Abstract

In this survey, we present a detailed guide on using the computer algebra system OSCAR to compute monomial bases for simple, finite-dimensional modules of simple, complex Lie algebras. We will also demonstrate how to determine monomial bases for the homogeneous coordinate ring of a (partial) flag variety, depending on a chosen birational sequence and a monomial order. This survey will be updated to reflect any advancements in OSCAR's capabilities in these areas.

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Xin Fang, Ghislain Fourier, Lars Göttgens, Ben Wilop. 2024-03-22. Computing monomial bases in Lie theory using OSCAR. https://arxiv.org/abs/2403.15018

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