LieART 2.0 -- a Mathematica application for Lie algebras and representation theory

DOI10.1016/j.cpc.2020.107490zbMath1515.17005arXiv1912.10969OpenAlexW4230919088MaRDI QIDQ6155969

Robert J. Saskowski, Robert Feger, Thomas W. Kephart

Publication date: 7 June 2023

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.10969

zbMATH Keywords

irreducible representationLie algebraLie groupmodel buildingrepresentation theorytensor productbranching rule

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Computational methods for problems pertaining to nonassociative rings and algebras (17-08) Software, source code, etc. for problems pertaining to nonassociative rings and algebras (17-04) Root systems (17B22) Computational methods for problems pertaining to topological groups (22-08)

Related Items (10)

Infrared phases of \(2d\) QCD ⋮ Trinification from \(\mathrm{E}_6\) symmetry breaking ⋮ Higher Flavor Symmetries in the Standard Model ⋮ GroupMath: a Mathematica package for group theory calculations ⋮ Eigenvalues and eigenforms on Calabi-Yau threefolds ⋮ Tree-level amplitudes from the pure spinor superstring ⋮ Mixed moduli in 3d \(\mathcal{N} = 4\) higher-genus quivers ⋮ A survey of family unification models with bifundamental matter ⋮ Machine learning Lie structures \& applications to physics ⋮ Folding orthosymplectic quivers

Cites Work

• Origins of inert Higgs doublets
• \texttt{Affine.m} -- \texttt{Mathematica} package for computations in representation theory of finite-dimensional and affine Lie algebras
• BPS states in the Minahan-Nemeschansky \({E_6}\) theory
• On the chirality of the SM and the fermion content of GUTs
• Masses and mixing of neutral leptons in a grand unified \(E_6\) model with intermediate Pati-Salam symmetry
• Surveying the quantum group symmetries of integrable open spin chains
• The integrable quantum group invariant \(A_{2 n - 1}^{(2)}\) and \(D_{n + 1}^{(2)}\) open spin chains
• LieART -- a Mathematica application for Lie algebras and representation theory
• PyR{\@}TE 2: a Python tool for computing RGEs at two-loop
• Faster tensor canonicalization
• The maximal subgroups of the classical groups
• Semisimple subalgebras of semisimple Lie algebras
• Fast recursion formula for weight multiplicities
• Introduction to Lie Algebras and Representation Theory
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