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 106 articles )

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  1. Mukhopadhyay, Swarnava: Strange duality of Verlinde spaces for $G_2$ and $F_4$ (2016)
  2. Derksen, Harm; Kemper, Gregor: Computational invariant theory. With two appendices by Vladimir L. Popov and an addendum by Nobert A. Campo and Vladimir L. Popov (2015)
  3. Fernández Núñez, José; García Fuertes, Wifredo; Perelomov, Askold M.: Generating functions and multiplicity formulas: the case of rank two simple Lie algebras (2015)
  4. Leung, Naichung Conan; Zhang, Jiajin: Cox rings of rational surfaces and flag varieties of \itADE-types (2015)
  5. Li, Jian-Rong: On the extended T-system of type $C_3$ (2015)
  6. Bernig, Andreas; Solanes, Gil: Classification of invariant valuations on the quaternionic plane (2014)
  7. Dietrich, Heiko; Faccin, Paolo; de Graaf, Willem A.: A GAP package for computing with real semisimple Lie algebras (2014)
  8. Greenberg, Matthew; Voight, John: Lattice methods for algebraic modular forms on classical groups (2014)
  9. Iliev, Atanas; Manivel, Laurent: On cubic hypersurfaces of dimensions 7 and 8 (2014)
  10. Thiel, Ulrich: A counter-example to Martino’s conjecture about generic Calogero-Moser families. (2014)
  11. Achar, Pramod N.; Henderson, Anthony: Geometric Satake, Springer correspondence and small representations (2013)
  12. Bruns, Winfried; Conca, Aldo; Varbaro, Matteo: Relations between the minors of a generic matrix (2013)
  13. Dietrich, Heiko; Faccin, Paolo; de Graaf, Willem A.: Computing with real Lie algebras: real forms, Cartan decompositions, and Cartan subalgebras (2013)
  14. García-Etxebarria, Iñaki; Heidenreich, Ben; Wrase, Timm: New $ \mathcalN = 1$ dualities from orientifold transitions part I: field theory (2013)
  15. Gruson, Laurent; Sam, Steven V.; Weyman, Jerzy: Moduli of abelian varieties, Vinberg $\theta$-groups, and free resolutions (2013)
  16. Hague, Chuck; McNinch, George: Some good-filtration subgroups of simple algebraic groups. (2013)
  17. Pecher, Tobias: Multiplicity-free super vector spaces. (2013)
  18. Cartwright, Dustin A.; Erman, Daniel; Oeding, Luke: Secant varieties of $\bbfP^2 \times \bbfP^n$ embedded by $\cal O(1,2)$ (2012)
  19. Draisma, Jan: Transitive Lie algebras of vector fields: an overview (2012)
  20. Ivanov, Kamen; Petrushev, Pencho; Xu, Yuan: Decomposition of spaces of distributions induced by tensor product bases (2012)

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