Noncommutative symmetric functions and laplace operators for classical Lie algebras
Copyright policy )Noncommutative symmetric functions and laplace operators for classical Lie algebras
New systems of Laplace (Casimir) operators for the orthogonal and symplectic Lie algebras are constructed. The operators are expressed in terms of paths in graphs related to matrices formed by the generators of these Lie algebras with the use of some properties of the noncommutative symmetric functions associated with a matrix. The decomposition of the Sklyanin determinant into a product of quasi-determinants play the main role in the construction. Analogous decomposition for the quantum determinant provides an alternative proof of the known construction for the Lie algebra gl(N).
25 pages
- Australian National University Australia
High Energy Physics - Theory, Symmetric functions and generalizations, Sklyanin determinant, FOS: Physical sciences, Quantum groups (quantized enveloping algebras) and related deformations, Casimir operators, quasi-determinants, High Energy Physics - Theory (hep-th), Laplace operators, Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), noncommutative symmetric functions, quantum determinant, Universal enveloping (super)algebras, Quantum groups and related algebraic methods applied to problems in quantum theory, symplectic Lie algebras
High Energy Physics - Theory, Symmetric functions and generalizations, Sklyanin determinant, FOS: Physical sciences, Quantum groups (quantized enveloping algebras) and related deformations, Casimir operators, quasi-determinants, High Energy Physics - Theory (hep-th), Laplace operators, Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), noncommutative symmetric functions, quantum determinant, Universal enveloping (super)algebras, Quantum groups and related algebraic methods applied to problems in quantum theory, symplectic Lie algebras
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