Noncommutative symmetric functions and Laplace operators for classical Lie algebras

Details Noncommutative symmetric functions and Laplace operators for classical Lie algebras Noncommutative symmetric functions and Laplace operators for classical Lie algebras

1994-09-16

arxiv.org/abs/hep-th/9409090v1

Lett.Math.Phys. 35 (1995) 135-143

Physics

High Energy Physics

High Energy Physics - Theory

25 pages

Scientific paper

10.1007/BF00750763

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).

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