Noncanonical Polynomial Representations of Classical Lie Algebras

Abstract

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.

References in corpus (1)

• Flag Partial Differential Equations and Representations of Lie Algebras

Cited by in corpus (2)

• Polynomial Representation of $F_4$ and a New Combinatorial Identity about Twenty-Four
• Polynomial Representation of $E_7$ and Its Combinatorial and PDE Implications