LiE

LiE is the name of a software package that enables mathematicians and physicists to perform computations of a Lie group theoretic nature. It focuses on the representation theory of complex semisimple (reductive) Lie groups and algebras, and on the structure of their Weyl groups and root systems. LiE does not compute directly with elements of the Lie groups and algebras themselves; it rather computes with weights, roots, characters and similar objects. Some specialities of LiE are: tensor product decompositions, branching to subgroups, Weyl group orbits, reduced elements in Weyl groups, distinguished coset representatives and much more. These operations have been compiled into the program which results in fast execution: typically one or two orders of magnitude faster than similar programs written in a general purpose program. The LiE programming language makes it possible to customise and extend the package with more mathematical functions. A user manual is provided containing many examples. LiE establishes an interactive environment from which commands can be given that involve basic programming primitives and powerful built-in functions. These commands are read by an interpreter built into the package and passed to the core of the system. This core consists of programs representing some 100 mathematical functions. The interpreter offers on-line facilities which explain operations and functions, and which give background information about Lie group theoretical concepts and about currently valid definitions and values. Computer algebra system (CAS).

This software is also referenced in ORMS.


References in zbMATH (referenced in 158 articles )

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  1. Abuaf, Roland: On quartic double fivefolds and the matrix factorizations of exceptional quaternionic representations (2021)
  2. Abuaf, Roland; Manivel, Laurent: Gradings of Lie algebras, magical spin geometries and matrix factorizations (2021)
  3. Avdeev, Roman; Petukhov, Alexey: Spherical actions on isotropic flag varieties and related branching rules (2021)
  4. Gates, S. James jun.; Hu, Yangrui; Mak, S.-N. Hazel: Weyl covariance, and proposals for superconformal prepotentials in 10D superspaces (2021)
  5. Avdeev, Roman; Petukhov, Alexey: Branching rules related to spherical actions on flag varieties (2020)
  6. Bendel, C. P.; Nakano, D. K.; Pillen, C.; Sobaje, P.: On tensoring with the Steinberg representation (2020)
  7. Benedetti, Vladimiro; Filippini, Sara Angela; Manivel, Laurent; Tanturri, Fabio: Orbital degeneracy loci and applications (2020)
  8. Gui, Bin: Polynomial energy bounds for type (F_4) WZW-models (2020)
  9. Halawi, Hezi; Segal, Avner: The degenerate principal series representations of exceptional groups of type (E_6) over (p)-adic fields (2020)
  10. Herbig, Hans-Christian; Schwarz, Gerald W.; Seaton, Christopher: Symplectic quotients have symplectic singularities (2020)
  11. Lercier, Reynald; Ritzenthaler, Christophe; Sijsling, Jeroen: Reconstructing plane quartics from their invariants (2020)
  12. Makhlin, Igor: PBW degenerate Schubert varieties: Cartan components and counterexamples (2020)
  13. Renato M. Fonseca: GroupMath: A Mathematica package for group theory calculations (2020) arXiv
  14. Gomis, Joaquim; Kleinschmidt, Axel; Palmkvist, Jakob: Symmetries of M-theory and free Lie superalgebras (2019)
  15. Knop, Friedrich; Krötz, Bernhard; Pecher, Tobias; Schlichtkrull, Henrik: Classification of reductive real spherical pairs. I: The simple case (2019)
  16. Kulyabov, D. S.; Korol’kova, A. V.; Sevast’yanov, L. A.: New features in the second version of the Cadabra computer algebra system (2019)
  17. Mafra, Carlos R.; Schlotterer, Oliver: Towards the n-point one-loop superstring amplitude. I: Pure spinors and superfield kinematics (2019)
  18. Barthel, Tobias (ed.); Krause, Henning (ed.); Stojanoska, Vesna (ed.): Mini-workshop: Chromatic phenomena and duality in homotopy theory and representation theory. Abstracts from the mini-workshop held March 4--10, 2018 (2018)
  19. Benedetti, Vladimiro: Manifolds of low dimension with trivial canonical bundle in Grassmannians (2018)
  20. Diamond, Benjamin E.: Smooth surfaces in smooth fourfolds with vanishing first Chern class (2018)

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