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LieART 2.0 -- A Mathematica Application for Lie Algebras and Representation Theory

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arxiv 1912.10969 v2 pith:TBN7MZZQ submitted 2019-12-20 hep-th hep-phmath-phmath.GRmath.MPmath.RT

Robert Feger , Thomas W. Kephart , Robert J. Saskowski This is my paper · ORCID
classification hep-thhep-phmath-phmath.GRmath.MPmath.RT
keywords algebraslieartbranchingirreduciblemathematicarepresentationrepresentationstheory
verification ladder T0 review T1 audit T2 compute T3 formal
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We present LieART 2.0 which contains substantial extensions to the Mathematica application LieART (Lie Algebras and Representation Theory) for computations frequently encountered in Lie algebras and representation theory, such as tensor product decomposition and subalgebra branching of irreducible representations. The basic procedure is unchanged: it computes root systems of Lie algebras, weight systems and several other properties of irreducible representations, but new features and procedures have been included to allow the extensions to be seamless. The new version of LieART continues to be user friendly. New extended tables of properties, tensor products and branching rules of irreducible representations are included in the supplementary material for use without Mathematica software. LieART 2.0 now includes the branching rules to special subalgebras for all classical and exceptional Lie algebras up to and including rank 15.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Global anomalies in $6D$ gauged supergravities

    hep-th 2025-07 conditional novelty 7.0 of 10

    New anomaly-free six-dimensional R-symmetry gauged supergravities are presented, and global anomaly freedom is shown to impose the constraints n_V ≡ 8 mod 12 (U(1)_R) and n_V = 60 (Sp(1)_R).

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    For 5d N=1 pure gauge theories, Wilson-loop blowup equations can be fixed using one-form symmetry and low-instanton data, and one-instanton free energies admit a universal v=sqrt(q1q2) expansion resembling Hilbert series.

  4. 4D de Sitter from 6D gauged supergravity with Green-Schwarz counterterm

    hep-th 2025-10 conditional novelty 6.0 of 10

    6D gauged supergravity with the Green-Schwarz counterterm admits exact dS4×S2 and Mink4×S2 solutions (with a monopole); the de Sitter vacuum has two tachyons and flows to Minkowski.

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