Computing monomial bases in Lie theory using OSCAR

2024/03/22 by Fang, Xin, Fourier, Ghislain, Göttgens, Lars +1
#14-04 #14D06 #14M15 #14M25 #17B10 #97N80 #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2403.15018

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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