Sklyanin determinant, Laplace operators, and characteristic identities for classical Lie algebras

DOI10.1063/1.531366zbMath0861.17009OpenAlexW2005088245MaRDI QIDQ4837398

Alexander I. Molev

Publication date: 3 July 1995

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

Full work available at URL: https://doi.org/10.1063/1.531366

zbMATH Keywords

generatorsquantum Yang-Baxter equationquantized enveloping algebrastwisted YangiansSklyanin determinantquantum determinant

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Ring-theoretic aspects of quantum groups (16T20) Yang-Baxter equations and Rota-Baxter operators (17B38)

Related Items

Unnamed Item, Two determinants in the universal enveloping algebras of the orthogonal Lie algebras, Generalized symmetrization in enveloping algebras, Quantum matrix algebras of BMW type: structure of the characteristic subalgebra, Stirling partitions of the symmetric group and Laplace operators for the orthogonal Lie algebra, Bethe subalgebras in twisted Yangians, Central elements in the universal enveloping algebras for the split realization of the orthogonal Lie algebras, A note on constructing quasi modules for quantum vertex algebras from twisted Yangians, On Segal-Sugawara vectors and Casimir elements for classical Lie algebras, TWISTED YANGIANS AND FOLDED ${\mathcal W}$ -ALGEBRAS, Deformation of YangianY(sl₂), Capelli identities for reductive dual pairs, A Cayley-Hamilton theorem for the skew Capelli elements, Finite-dimensional irreducible representations of twisted Yangians, TWO PERMANENTS IN THE UNIVERSAL ENVELOPING ALGEBRAS OF THE SYMPLECTIC LIE ALGEBRAS

Cites Work

• Quantum Berezinian and the classical Capelli identity
• The Capelli identity, the double commutant theorem, and multiplicity-free actions
• A new interpretation of Gelfand-Tsetlin bases
• Gelfand-Tsetlin basis for representations of Yangians
• Characteristic identities for semi-simple Lie algebras
• Characteristic Identities for Generators of GL(n), O(n) and Sp(n)