Capelli identities for Lie superalgebras

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Publication details

JournalAnnales scientifiques de l ecole normale superieure
DatePublished - 1997
Issue number6
Number of pages26
Pages (from-to)847-872
Original languageEnglish


We study a distinguished basis in the centre of the enveloping algebra of the Lie superalgebra q(N). The irreducible polynomial representations of q(N) are labelled by decreasing sequences of positive integers lambda = (lambda(1),...,lambda(l)) with l less than or equal to N. The elements of our basis are labelled by the same sequences. The basic element C-lambda of the centre vanishes in the irreducible representation corresponding to a sequence mu if and only if lambda(i) > mu(i) for some i. We obtain an explicit formula for the element C-lambda.

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