Central elements in the universal enveloping algebras for the split realization of the orthogonal Lie algebras

DOI10.1007/s11005-006-0082-6zbMath1118.17002OpenAlexW2049486543MaRDI QIDQ883179

Akihito Wachi

Publication date: 31 May 2007

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11005-006-0082-6

zbMATH Keywords

column determinantorthogonal Lie algebracentral elementsplit realization

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Universal enveloping (super)algebras (17B35)

Related Items (8)

Two determinants in the universal enveloping algebras of the orthogonal Lie algebras ⋮ JACOBI-TRUDI FORMULA FOR THE HIGHER CAPELLI ELEMENTS OF CLASSICAL LIE ALGEBRAS ⋮ THE DESCRIPTION OF THE CAPELLI ELEMENTS WITH A PARAMETER FOR CLASSICAL LIE ALGEBRAS IN TERMS OF SYMMETRIZED DETERMINANT ⋮ Casimir elements from the Brauer-Schur-Weyl duality ⋮ On Segal-Sugawara vectors and Casimir elements for classical Lie algebras ⋮ Intersection of harmonics and Capelli identities for symmetric pairs ⋮ TWO PERMANENTS IN THE UNIVERSAL ENVELOPING ALGEBRAS OF THE SYMPLECTIC LIE ALGEBRAS ⋮ Extensions of the Tensor Algebra and Their Applications

Cites Work

• The Capelli identity, the double commutant theorem, and multiplicity-free actions
• Capelli identities for classical Lie algebras
• TWO PERMANENTS IN THE UNIVERSAL ENVELOPING ALGEBRAS OF THE SYMPLECTIC LIE ALGEBRAS
• Yangians and classical Lie algebras
• Sklyanin determinant, Laplace operators, and characteristic identities for classical Lie algebras
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