Capelli identities for lie superalgebras

DOI10.1016/S0012-9593(97)89941-7zbMath0892.17011arXivq-alg/9610032OpenAlexW1971468620MaRDI QIDQ4376760

M. L. Nazarov

Publication date: 5 August 1998

Published in: Annales Scientifiques de l’École Normale Supérieure (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/q-alg/9610032

zbMATH Keywords

universal enveloping algebrassimple Lie superalgebrasCapelli identitiesinvariant theory of Lie superalgebras

Mathematics Subject Classification ID

Universal enveloping (super)algebras (17B35) Vector and tensor algebra, theory of invariants (15A72) Superalgebras (17A70) Universal enveloping algebras of Lie algebras (16S30)

Related Items (10)

Multiparameter universal characters of B-type and integrable hierarchy ⋮ Linear transformations of vertex operators of Hall-Littlewood polynomials ⋮ Howe duality and combinatorial character formula for orthosymplectic Lie superalgebras. ⋮ Quasi-finite modules for Lie superalgebras of infinite rank ⋮ A Generalization of the Capelli Identity ⋮ Highest weight modules over quantum queer superalgebra \(U_q(\mathfrak {q}(n))\) ⋮ The Capelli eigenvalue problem for Lie superalgebras ⋮ Schur 𝑄-functions and the Capelli eigenvalue problem for the Lie superalgebra \ger𝑞(𝑛) ⋮ The structure of the Young symmetrizers for spin representations of the symmetric group. I ⋮ Multiparameter Schur \(Q\)-functions are solutions of the BKP hierarchy

Cites Work

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• The \(A_ n^{(1)}\) face models
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• Symmetric polynomials and the center of the symmetric group ring
• Quantum immanants and higher Capelli identities
• Dimensions of skew-shifted Young diagrams and projective characters of the infinite symmetric group
• THE TENSOR ALGEBRA OF THE IDENTITY REPRESENTATION AS A MODULE OVER THE LIE SUPERALGEBRAS $ \mathfrak{Gl}(n,\,m)$ AND $ Q(n)$
• Remarks on Classical Invariant Theory
• Lie superalgebras

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