About: Littelmann path model

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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.

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rdf:type	yago:WikicatLieAlgebras yago:Abstraction100002137 yago:Algebra106012726 yago:Cognition100023271 yago:Content105809192 yago:Discipline105996646 yago:KnowledgeDomain105999266 yago:Mathematics106000644 yago:PsychologicalFeature100023100 yago:PureMathematics106003682 device yago:Science105999797
rdfs:label	Littelmann path model (en)
rdfs: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. 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. (en)
dcterms:subject	Algebraic combinatorics Lie algebras Representation theory
Wikipage page ID	11167326 (xsd:integer)
Wikipage revision ID	1052635644 (xsd:integer)
Link from a Wikipage to another Wikipage	Representation theory Bertram Kostant Algebraic combinatorics Richard Brauer Levi decomposition Robert Steinberg Lie algebras Masaki Kashiwara Mathematics General linear group Standard monomial theory George Lusztig Monomial representation Root lattice Littlewood–Richardson rule Combinatorics Dominant weight C. S. Seshadri Graduate Studies in Mathematics Graph theory Hans Freudenthal Kac–Moody algebra Universal enveloping algebra Hermann Weyl Issai Schur Representation theory Cartan subalgebra Semisimple Lie group Young tableau Root system Special linear group Quantum group Semisimple Lie algebra Schubert variety Weyl character formula Weyl group Peter Littelmann Parabolic subalgebra Weyl chamber Branching rule Crystal basis Weight lattice
Link from a Wikipage to an external page	https://archive.org/details/introductiontoli00jame https://books.google.com/books%3Fid=2twDDAAAQBAJ http://www.numdam.org/numdam-bin/fitem%3Fid=SB_1994-1995__37__209_0%7Cyear=1995 https://books.google.com/books%3Fid=C6xHHEaI-GcC https://books.google.com/books%3Fid=srv90XiUbZoC
sameAs	Littelmann path model Littelmann path model Littelmann path model Littelmann path model
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has 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 Lusztig using quantum groups. (en)
gold:hypernym	Device
prov:wasDerivedFrom	wikipedia-en:Littelmann_path_model?oldid=1052635644&ns=0
page length (characters) of wiki page	15779 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Littelmann_path_model
is Link from a Wikipage to another Wikipage of	Standard monomial theory Glossary of representation theory Littlewood–Richardson rule Quantum affine algebra Restricted representation Peter Littelmann Path model Littelmann path Littelmann paths Littleman path
is Wikipage redirect of	Path model Littelmann path Littelmann paths Littleman path
is foaf:primaryTopic of	wikipedia-en:Littelmann_path_model

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