The coxeter and weyl Packages. The coxeter package contains 38 Maple procedures for working with root systems and finite Coxeter groups. It provides facilities for manipulating roots, reflections, reduced expressions, for generating permutation representations and irreducible characters of finite Coxeter groups, and for retrieving information such as one finds in the appendices of Bourbaki. The weyl subpackage provides 12 additional procedures for manipulating weights and characters of irreducible representations of semisimple Lie algebras, including functions for computing weight multiplicities, tensor product decompositions, and branching.

References in zbMATH (referenced in 22 articles )

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  1. Barnard, Emily: The canonical join complex (2019)
  2. Reading, Nathan: Lattice homomorphisms between weak orders (2019)
  3. Barnard, Emily; Reading, Nathan: Coxeter-bicatalan combinatorics (2018)
  4. La Scala, Roberto; Tiwari, Sharwan K.: Multigraded Hilbert series of noncommutative modules (2018)
  5. Petersen, T. Kyle: A two-sided analogue of the Coxeter complex (2018)
  6. Blanco, Saúl A.: Shortest path poset of Bruhat intervals (2013)
  7. Krattenthaler, Christian; Müller, Thomas W.: Cyclic sieving for generalised non-crossing partitions associated with complex reflection groups of exceptional type (2013)
  8. Nazarov, Anton: \textttAffine.m -- \textttMathematicapackage for computations in representation theory of finite-dimensional and affine Lie algebras (2012)
  9. Drton, Mathias; Klivans, Caroline J.: A geometric interpretation of the characteristic polynomial of reflection arrangements (2010)
  10. Krattenthaler, C.; Müller, T. W.: Decomposition numbers for finite Coxeter groups and generalised non-crossing partitions (2010)
  11. Petrov, Viktor; Semenov, Nikita: Generically split projective homogeneous varieties (2010)
  12. Armstrong, Drew: Generalized noncrossing partitions and combinatorics of Coxeter groups (2009)
  13. Hultman, Axel: Twisted identities in Coxeter groups. (2008)
  14. Krattenthaler, Christian: The (F)-triangle of the generalised cluster complex (2006)
  15. Krattenthaler, Christian: The (M)-triangle of generalised non-crossing partitions for the types (E_7) and (E_8). (2005)
  16. Stembridge, John R.: Explicit matrices for irreducible representations of Weyl groups. (2004)
  17. Hultman, Axel: Bruhat intervals of length 4 in Weyl groups. (2003)
  18. Krattenthaler, Christian; Orsina, Luigi; Papi, Paolo: Enumeration of ad-nilpotent (\mathfrakb)-ideals for simple Lie algebras (2002)
  19. Helminck, Aloysius G.: Computing orbits of minimal parabolic (k)-subgroups acting on symmetric (k)-varieties (2000)
  20. Joyner, D.; Martin, Roland: A Maple package for the decomposition of certain tensor products and restrictions of representations using crystal graphs (1998)

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