Extensions of the Tensor Algebra and Their Applications

DOI10.1080/00927872.2011.590952zbMath1271.15008arXiv0909.5586OpenAlexW2122445697MaRDI QIDQ3145446

Minoru Itoh

Publication date: 20 December 2012

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.5586

zbMATH Keywords

Weyl algebrasymmetric grouprepresentation theorycanonical commutation relationsClifford algebrainvariant theorySchur-Weyl dualityCapelli identitytensor algebraquantum immanantscentral elements of universal enveloping algebras

Mathematics Subject Classification ID

Determinants, permanents, traces, other special matrix functions (15A15) Representations of finite symmetric groups (20C30) Universal enveloping (super)algebras (17B35) Vector and tensor algebra, theory of invariants (15A72) Commutativity of matrices (15A27) Clifford algebras, spinors (15A66)

Related Items (3)

THE DESCRIPTION OF THE CAPELLI ELEMENTS WITH A PARAMETER FOR CLASSICAL LIE ALGEBRAS IN TERMS OF SYMMETRIZED DETERMINANT ⋮ Twisted immanant and matrices with anticommuting entries ⋮ A \(q\)-analogue of derivations on the tensor algebra and the \(q\)-Schur-Weyl duality

Cites Work

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• Capelli identities for reductive dual pairs
• Quantum Berezinian and the classical Capelli identity
• The Capelli identity, the double commutant theorem, and multiplicity-free actions
• Central elements in the universal enveloping algebras for the split realization of the orthogonal Lie algebras
• Capelli identities for classical Lie algebras
• Application of Koszul complex to Wronski relations for \(U(\mathfrak{gl}_n)\)
• Capelli identities for the dual pair \((\text{O}_M,\text{Sp}_N)\)
• Symmetric polynomials and the center of the symmetric group ring
• Quantum immanants and higher Capelli identities
• Two determinants in the universal enveloping algebras of the orthogonal Lie algebras
• On the Proof of the Capelli Identities
• TWO PERMANENTS IN THE UNIVERSAL ENVELOPING ALGEBRAS OF THE SYMPLECTIC LIE ALGEBRAS
• Newton’s formula for 𝔤𝔩_{𝔫}
• On Turnbull identity for skew-symmetric matrices
• A Cayley-Hamilton theorem for the skew Capelli elements

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