Capelli identities for Lie superalgebras

Maxim Nazarov

Capelli identities for Lie superalgebras

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	847-872
Number of pages	26
Journal	Annales scientifiques de l ecole normale superieure
Volume	30
Issue number	6
Publication status	Published - 1997

Keywords

ENVELOPING ALGEBRA

Access to Document

http://arxiv.org/abs/q-alg/9610032

Cite this

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title = "Capelli identities for Lie superalgebras",

abstract = "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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AU - Nazarov, Maxim

PY - 1997

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N2 - 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.

AB - 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.

KW - ENVELOPING ALGEBRA

M3 - Article

SN - 0012-9593

VL - 30

SP - 847

EP - 872

JO - Annales scientifiques de l ecole normale superieure

JF - Annales scientifiques de l ecole normale superieure

IS - 6

ER -