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 15 articles )

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  1. Apruzzi, Fabio; Fazzi, Marco: $\mathrmAdS_7/\mathrmCFT_6$ with orientifolds (2018)
  2. Mukhi, Sunil; Muralidhara, Girish: Universal RCFT correlators from the holomorphic bootstrap (2018)
  3. Ahmed, Ibrahim; Nepomechie, Rafael I.; Wang, Chunguang: Quantum group symmetries and completeness for $A_2n^(2)$ open spin chains (2017)
  4. Hayashi, Hirotaka; Ohmori, Kantaro: 5d/6d DE instantons from trivalent gluing of web diagrams (2017)
  5. Hollands, Lotte; Neitzke, Andrew: BPS states in the Minahan-Nemeschansky $E_6$ theory (2017)
  6. Lysenko, Sergey: Twisted Whittaker models for metaplectic groups (2017)
  7. Moriyama, Sanefumi; Nosaka, Tomoki; Yano, Katsuya: Superconformal Chern-Simons theories from del Pezzo geometries (2017)
  8. Nepomechie, Rafael I.; Pimenta, Rodrigo A.; Retore, Ana L.: The integrable quantum group invariant $A_2 n - 1^(2)$ and $D_n + 1^(2)$ open spin chains (2017)
  9. Hahn, Heekyoung: On tensor third $L$-functions of automorphic representations of $\mathrmGL_n(\mathbb A_F)$ (2016)
  10. Feger, Robert; Kephart, Thomas W.: LieART -- a Mathematica application for Lie algebras and representation theory (2015)
  11. Fonseca, Renato M.: On the chirality of the SM and the fermion content of GUTs (2015)
  12. Matassa, Marco: An analogue of Weyl’s law for quantized irreducible generalized flag manifolds (2015)
  13. Hanany, Amihay; Kalveks, Rudolph: Highest weight generating functions for Hilbert series (2014)
  14. de Medeiros, Paul; Hollands, Stefan: Superconformal quantum field theory in curved spacetime (2013)
  15. Hofmann, M.; Rudolph, G.; Schmidt, M.: On the reflection type decomposition of the adjoint reduced phase space of a compact semisimple Lie group (2013)