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Statements

Subject Item: dbr:Length_function
dbo:wikiPageWikiLink: dbr:Length_of_a_Weyl_group_element

Subject Item: dbr:Length_of_a_Weyl_group_element
rdf:type: owl:Thing dbo:School yago:WikicatLieGroups yago:Abstraction100002137 yago:Group100031264
rdfs:label: Length of a Weyl group element
rdfs:comment: In mathematics, the length of an element w in a Weyl group W, denoted by l(w), is the smallest number k so that w is a product of k reflections by simple roots. (So, the notion depends on the choice of a positive Weyl chamber.) In particular, a simple reflection has length one. The function l is then an integer-valued function of W; it is a length function of W. It follows immediately from the definition that l(w−1) = l(w) and that l(ww'−1) ≤ l(w) + l(w' ).(See also: Longest element of a Coxeter group)
rdfs:seeAlso: dbr:Longest_element_of_a_Coxeter_group
dcterms:subject: dbc:Lie_groups
dbo:wikiPageID: 39251565
dbo:wikiPageRevisionID: 1002418775
dbo:wikiPageWikiLink: dbr:Positive_Weyl_chamber dbc:Lie_groups dbr:Weyl_group dbr:Length_function
owl:sameAs: wikidata:Q16937449 freebase:m.0t_dxpw yago-res:Length_of_a_Weyl_group_element n17:f4Qr
dbp:wikiPageUsesTemplate: dbt:See_also dbt:Cite_book
dbo:abstract: In mathematics, the length of an element w in a Weyl group W, denoted by l(w), is the smallest number k so that w is a product of k reflections by simple roots. (So, the notion depends on the choice of a positive Weyl chamber.) In particular, a simple reflection has length one. The function l is then an integer-valued function of W; it is a length function of W. It follows immediately from the definition that l(w−1) = l(w) and that l(ww'−1) ≤ l(w) + l(w' ).(See also: Longest element of a Coxeter group)
gold:hypernym: dbr:K
prov:wasDerivedFrom: wikipedia-en:Length_of_a_Weyl_group_element?oldid=1002418775&ns=0
dbo:wikiPageLength: 875
foaf:isPrimaryTopicOf: wikipedia-en:Length_of_a_Weyl_group_element

Subject Item: dbr:List_of_things_named_after_Hermann_Weyl
dbo:wikiPageWikiLink: dbr:Length_of_a_Weyl_group_element

Subject Item: dbr:Weyl_integration_formula
dbo:wikiPageWikiLink: dbr:Length_of_a_Weyl_group_element

Subject Item: dbr:Weyl_group
dbo:wikiPageWikiLink: dbr:Length_of_a_Weyl_group_element

Subject Item: dbr:Length_function_of_a_Weyl_group_element
dbo:wikiPageWikiLink: dbr:Length_of_a_Weyl_group_element
dbo:wikiPageRedirects: dbr:Length_of_a_Weyl_group_element

Subject Item: dbr:Length_of_a_Weyl_element
dbo:wikiPageWikiLink: dbr:Length_of_a_Weyl_group_element
dbo:wikiPageRedirects: dbr:Length_of_a_Weyl_group_element

Subject Item: wikipedia-en:Length_of_a_Weyl_group_element
foaf:primaryTopic: dbr:Length_of_a_Weyl_group_element