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Satake diagrams, Iwasawa and Langlands decompositions of classical Lie superalgebras A(m,n), B(m,n) and D(m,n) - MaRDI portal

Satake diagrams, Iwasawa and Langlands decompositions of classical Lie superalgebras A(m,n), B(m,n) and D(m,n) (Q1115515)

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scientific article; zbMATH DE number 4085870
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English
Satake diagrams, Iwasawa and Langlands decompositions of classical Lie superalgebras A(m,n), B(m,n) and D(m,n)
scientific article; zbMATH DE number 4085870

    Statements

    Satake diagrams, Iwasawa and Langlands decompositions of classical Lie superalgebras A(m,n), B(m,n) and D(m,n) (English)
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    1988
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    The authors generalize the Iwasawa decompositions and the Satake diagrams of the real semi-simple Lie algebras as well as the Langlands decompositions of their parabolic subalgebras to the special linear and the orthosymplectic Lie superalgebras. Unfortunately, the authors do not completely specify their notation (which is largely taken from their references 4, 8, and 9), more importantly, they do not say what they mean by a compact Lie superalgebra. Since this notion is certainly fundamental to the theory, and since the paper does not contain any proofs, I am unable to find out what the authors really have done.
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    Iwasawa decompositions
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    Satake diagrams
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    Langlands decompositions
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    parabolic subalgebras
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    special linear
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    orthosymplectic Lie superalgebras
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    compact Lie superalgebra
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