LieART

LieART - A Mathematica Application for Lie Algebras and Representation Theory. We present 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. LieART can handle all classical and exceptional Lie algebras. It computes root systems of Lie algebras, weight systems and several other properties of irreducible representations. LieART’s user interface has been created with a strong focus on usability and thus allows the input of irreducible representations via their dimensional name, while the output is in the textbook style used in most particle-physics publications. The unique Dynkin labels of irreducible representations are used internally and can also be used for input and output. LieART exploits the Weyl reflection group for most of the calculations, resulting in fast computations and a low memory consumption. Extensive tables of properties, tensor products and branching rules of irreducible representations are included in the appendix.


References in zbMATH (referenced in 58 articles )

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  1. Braun, Andreas P.; Chen, Jin; Haghighat, Babak; Sperling, Marcus; Yang, Shuhang: Fibre-base duality of 5d KK theories (2021)
  2. Chen, Heng-Yu; He, Yang-Hui; Lal, Shailesh; Majumder, Suvajit: Machine learning Lie structures & applications to physics (2021)
  3. Dupuis, Éric; Witczak-Krempa, William: Monopole hierarchy in transitions out of a Dirac spin liquid (2021)
  4. Fendley, Paul: Integrability and braided tensor categories (2021)
  5. Gates, S. James jun.; Hu, Yangrui; Mak, S.-N. Hazel: Weyl covariance, and proposals for superconformal prepotentials in 10D superspaces (2021)
  6. Hadasz, Leszek; Ruba, Błażej: Airy structures for semisimple Lie algebras (2021)
  7. Hayashi, Hirotaka; Kim, Hee-Cheol; Ohmori, Kantaro: 6d/5d exceptional gauge theories from web diagrams (2021)
  8. Isaev, A. P.; Krivonos, S. O.: Split Casimir operator for simple Lie algebras, solutions of Yang-Baxter equations, and Vogel parameters (2021)
  9. Isaev, A. P.; Provorov, A. A.: Projectors on invariant subspaces of representations (\textad^\otimes2) of Lie algebras (so(N)) and (sp(2r)) and Vogel parameterization (2021)
  10. James Gates, S. jun.; Hu, Yangrui; Mak, S.-N. Hazel: Component decompositions and adynkra libraries for supermultiplets in lower dimensional superspaces (2021)
  11. Kashani-Poor, Amir-Kian: Determining F-theory matter via Gromov-Witten invariants (2021)
  12. Nepomechie, Rafael I.; Retore, Ana L.: Spin chains with boundary inhomogeneities (2021)
  13. Oehlmann, Paul-Konstantin: Non-flat elliptic four-folds, three-form cohomology and strongly coupled theories in four dimensions (2021)
  14. Pilch, Krzysztof; Walker, Robert; Warner, Nicholas P.: Separability in consistent truncations (2021)
  15. Avetisyan, M. Y.; Mkrtchyan, R. L.: On ((\mathrmad)^n(X_2)^k) series of universal quantum dimensions (2020)
  16. Gates, S. James jun.; Hu, Yangrui; Mak, S.-N. Hazel: Superfield component decompositions and the scan for prepotential supermultiplets in 10D superspaces (2020)
  17. Gimenez-Grau, Aleix; Kristjansen, Charlotte; Volk, Matthias; Wilhelm, Matthias: A quantum framework for AdS/dCFT through fuzzy spherical harmonics on (S^4) (2020)
  18. Hasebe, Kazuki: (SO(5)) Landau models and nested Nambu matrix geometry (2020)
  19. Renato M. Fonseca: GroupMath: A Mathematica package for group theory calculations (2020) arXiv
  20. Agarwal, Prarit: On dimensional reduction of 4d $ \mathcalN=1 $ Lagrangians for Argyres-Douglas theories (2019)

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