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- Littelmann_path_model abstract "In mathematics, the Littelmann path model is a combinatorial device due to Peter Littelmann for computing multiplicities without overcounting in the representation theory of symmetrisable Kac–Moody algebras. Its most important application is to complex semisimple Lie algebras or equivalently compact semisimple Lie groups, the case described in this article. Multiplicities in irreducible representations, tensor products and branching rules can be calculated using a coloured directed graph, with labels given by the simple roots of the Lie algebra.Developed as a bridge between the theory of crystal bases arising from the work of Kashiwara and Lusztig on quantum groups and the standard monomial theory of C. S. Seshadri and Lakshmibai, Littelmann's path model associates to each irreducible representation a rational vector space with basis given by paths from the origin to a weight as well as a pair of root operators acting on paths for each simple root. This gives a direct way of recovering the algebraic and combinatorial structures previously discovered by Kashiwara and Lustzig using quantum groups.".
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- Littelmann_path_model wikiPageRevisionID "675193695".
- Littelmann_path_model wikiPageWikiLink Bertram_Kostant.
- Littelmann_path_model wikiPageWikiLink Branching_rule.
- Littelmann_path_model wikiPageWikiLink C._S._Seshadri.
- Littelmann_path_model wikiPageWikiLink Cartan_subalgebra.
- Littelmann_path_model wikiPageWikiLink Category:Algebraic_combinatorics.
- Littelmann_path_model wikiPageWikiLink Category:Lie_algebras.
- Littelmann_path_model wikiPageWikiLink Category:Representation_theory.
- Littelmann_path_model wikiPageWikiLink Combinatorics.
- Littelmann_path_model wikiPageWikiLink Crystal_base.
- Littelmann_path_model wikiPageWikiLink Crystal_basis.
- Littelmann_path_model wikiPageWikiLink Dominant_weight.
- Littelmann_path_model wikiPageWikiLink General_linear_group.
- Littelmann_path_model wikiPageWikiLink George_Lusztig.
- Littelmann_path_model wikiPageWikiLink Glossary_of_semisimple_groups.
- Littelmann_path_model wikiPageWikiLink Graduate_Studies_in_Mathematics.
- Littelmann_path_model wikiPageWikiLink Graph_theory.
- Littelmann_path_model wikiPageWikiLink Hans_Freudenthal.
- Littelmann_path_model wikiPageWikiLink Hermann_Weyl.
- Littelmann_path_model wikiPageWikiLink Issai_Schur.
- Littelmann_path_model wikiPageWikiLink Kac–Moody_algebra.
- Littelmann_path_model wikiPageWikiLink Levi_decomposition.
- Littelmann_path_model wikiPageWikiLink Littlewood–Richardson_rule.
- Littelmann_path_model wikiPageWikiLink Masaki_Kashiwara.
- Littelmann_path_model wikiPageWikiLink Mathematics.
- Littelmann_path_model wikiPageWikiLink Monomial_representation.
- Littelmann_path_model wikiPageWikiLink Parabolic_Lie_algebra.
- Littelmann_path_model wikiPageWikiLink Parabolic_subalgebra.
- Littelmann_path_model wikiPageWikiLink Peter_Littelmann.
- Littelmann_path_model wikiPageWikiLink Quantum_group.
- Littelmann_path_model wikiPageWikiLink Representation_theory.
- Littelmann_path_model wikiPageWikiLink Restricted_representation.
- Littelmann_path_model wikiPageWikiLink Richard_Brauer.
- Littelmann_path_model wikiPageWikiLink Robert_Steinberg.
- Littelmann_path_model wikiPageWikiLink Root_lattice.
- Littelmann_path_model wikiPageWikiLink Root_system.
- Littelmann_path_model wikiPageWikiLink Schubert_variety.
- Littelmann_path_model wikiPageWikiLink Semisimple_Lie_algebra.
- Littelmann_path_model wikiPageWikiLink Semisimple_Lie_group.
- Littelmann_path_model wikiPageWikiLink Special_linear_group.
- Littelmann_path_model wikiPageWikiLink Standard_monomial_theory.
- Littelmann_path_model wikiPageWikiLink Universal_enveloping_algebra.
- Littelmann_path_model wikiPageWikiLink Weight_(representation_theory).
- Littelmann_path_model wikiPageWikiLink Weight_lattice.
- Littelmann_path_model wikiPageWikiLink Weyl_chamber.
- Littelmann_path_model wikiPageWikiLink Weyl_character_formula.
- Littelmann_path_model wikiPageWikiLink Weyl_group.
- Littelmann_path_model wikiPageWikiLink Young_tableau.
- Littelmann_path_model wikiPageWikiLinkText "Littelmann path model".
- Littelmann_path_model wikiPageWikiLinkText "littelmann path model".
- Littelmann_path_model wikiPageWikiLinkText "path model".
- Littelmann_path_model hasPhotoCollection Littelmann_path_model.
- Littelmann_path_model wikiPageUsesTemplate Template:Citation.
- Littelmann_path_model wikiPageUsesTemplate Template:Harvtxt.
- Littelmann_path_model wikiPageUsesTemplate Template:Reflist.
- Littelmann_path_model subject Category:Algebraic_combinatorics.
- Littelmann_path_model subject Category:Lie_algebras.
- Littelmann_path_model subject Category:Representation_theory.
- Littelmann_path_model hypernym Device.
- Littelmann_path_model type Device.
- Littelmann_path_model type Algebra.
- Littelmann_path_model type Combinatoric.
- Littelmann_path_model type Field.
- Littelmann_path_model comment "In mathematics, the Littelmann path model is a combinatorial device due to Peter Littelmann for computing multiplicities without overcounting in the representation theory of symmetrisable Kac–Moody algebras. Its most important application is to complex semisimple Lie algebras or equivalently compact semisimple Lie groups, the case described in this article.".
- Littelmann_path_model label "Littelmann path model".
- Littelmann_path_model sameAs m.02r28l1.
- Littelmann_path_model sameAs Q6648763.
- Littelmann_path_model sameAs Q6648763.
- Littelmann_path_model wasDerivedFrom Littelmann_path_model?oldid=675193695.
- Littelmann_path_model isPrimaryTopicOf Littelmann_path_model.