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@prefix foaf: <http://xmlns.com/foaf/0.1/> .
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              The diamond cone was introduced by N. J. Wildberger for the Lie algebra sl(n;R). It is a combinatoric presentation for the space C[N] of polynomials functions on the nilpotent factor N in the Iwasawa decomposition of SL(n;R). This presentation describes the natural layering of this indecomposable N-module. This basis can be indexeded by using some semi standard Young tableaux. We realize the algebra C[N] as a quotient of the shape algebra S_ for SL(n;R). Let us call reduced shape algebra this quotient. It is possible to select a family of semi standard Young tableaux, the quasi standard tableaux, in such a manner to get a basis for the reduced shape algebra. In the present thesis, this construction is extended to the case of rank 2 semi simple Lie algebras, then to the cas of the Lie algebras sp(2n), finally, to the case of the super simple Lie algebra sl(m; 1). In each case, we define the quasi standard Young tableaux, and show they define a good basis for the reduced shape algebra, either directly, or using an adapted version of the jeu de taquin defined by Schützenberger.
            """ ;
    dct:identifier "NNT: 2010DIJOS080" ;
    dct:issued "2026-05-23T12:54:16.578764"^^xsd:dateTime ;
    dct:language "fr" ;
    dct:modified "2026-05-23T12:54:16.578769"^^xsd:dateTime ;
    dct:publisher <https://rec.harvest-normandie.data4citizen.com/organization/cce9db95-46d9-4dc2-84b6-764215d0a002> ;
    dct:title "Diamond cone" ;
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    dcat:keyword "algebres-de-lie-semi-simples-et-nilpotentes",
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        "no-english-keywords",
        "representations-et-algebre-de-forme",
        "tableaux-de-young",
        "tableaux-semi-standards-et-quasi-standards",
        "theses" ;
    dcat:landingPage <https://theses.hal.science/tel-00682548> .

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    dct:title "Diamond cone" ;
    dcat:accessURL <https://theses.hal.science/tel-00682548> .

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