Noncanonical Polynomial Representations of Classical Lie Algebras

Details Noncanonical Polynomial Representations of Classical Lie Algebras Noncanonical Polynomial Representations of Classical Lie Algebras

2008-04-02

arxiv.org/abs/0804.0305v2

Mathematics

Representation Theory

Scientific paper

Using the skew-symmetry of the differential operators and multiplication operators in the canonical representations of finite-dimensional classical Lie algebras, we obtain some noncanonical polynomial representations of the classical Lie algebras. The representation spaces of all polynomials are decomposed into irreducible submodules, which are infinite-dimensional. Bases for the irreducible submodules are constructed. In particular, we obtain some new infinite-dimensional irreducible modules of symplectic Lie algebras that are not of highest weight type.

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