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.

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  1. Fendley, Paul: Integrability and braided tensor categories (2021)
  2. Gates, S. James jun.; Hu, Yangrui; Mak, S.-N. Hazel: Weyl covariance, and proposals for superconformal prepotentials in 10D superspaces (2021)
  3. 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)
  4. Avetisyan, M. Y.; Mkrtchyan, R. L.: On ((a d)^n(X_2)^k) series of universal quantum dimensions (2020)
  5. Gates, S. James jun.; Hu, Yangrui; Mak, S.-N. Hazel: Superfield component decompositions and the scan for prepotential supermultiplets in 10D superspaces (2020)
  6. Gimenez-Grau, Aleix; Kristjansen, Charlotte; Volk, Matthias; Wilhelm, Matthias: A quantum framework for AdS/dCFT through fuzzy spherical harmonics on (S^4) (2020)
  7. Renato M. Fonseca: GroupMath: A Mathematica package for group theory calculations (2020) arXiv
  8. Agarwal, Prarit: On dimensional reduction of 4d $ \mathcalN=1 $ Lagrangians for Argyres-Douglas theories (2019)
  9. Apruzzi, Fabio; Hassler, Falk; Heckman, Jonathan J.; Rochais, Thomas B.: Nilpotent networks and 4D RG flows (2019)
  10. Córdova, Clay; Dumitrescu, Thomas T.; Intriligator, Kenneth: Multiplets of superconformal symmetry in diverse dimensions (2019)
  11. Kim, Joonho; Kim, Sung-Soo; Lee, Ki-Hong; Lee, Kimyeong; Song, Jaewon: Instantons from blow-up (2019)
  12. Nepomechie, Rafael I.; Retore, Ana L.: The spectrum of quantum-group-invariant transfer matrices (2019)
  13. Nii, Keita: Confinement in 3d $ \mathcalN=2$ Spin($N$) gauge theories with vector and spinor matters (2019)
  14. Apruzzi, Fabio; Fazzi, Marco: (\mathrmAdS_7/\mathrmCFT_6) with orientifolds (2018)
  15. Benli, Seçil; Dereli, Tekin: Masses and mixing of neutral leptons in a grand unified (E_6) model with intermediate Pati-Salam symmetry (2018)
  16. Cvetič, Mirjam; Heckman, Jonathan J.; Lin, Ling: Towards exotic matter and discrete non-abelian symmetries in F-theory (2018)
  17. Liendo, Pedro; Meneghelli, Carlo; Mitev, Vladimir: Bootstrapping the half-BPS line defect (2018)
  18. Mukhi, Sunil; Muralidhara, Girish: Universal RCFT correlators from the holomorphic bootstrap (2018)
  19. Nepomechie, Rafael I.; Pimenta, Rodrigo A.: New (\mathbfD_n+1^(2)) K-matrices with quantum group symmetry (2018)
  20. Nepomechie, Rafael I.; Retore, Ana L.: Surveying the quantum group symmetries of integrable open spin chains (2018)

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