Computing monomial bases in Lie theory using OSCAR
Representation Theory
2024-03-25 v1 Algebraic Geometry
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.
Cite
@article{arxiv.2403.15018,
title = {Computing monomial bases in Lie theory using OSCAR},
author = {Xin Fang and Ghislain Fourier and Lars Göttgens and Ben Wilop},
journal= {arXiv preprint arXiv:2403.15018},
year = {2024}
}
Comments
16 pages, Submitted as a bookchapter for the upcoming Oscar book