On Extensions of Conformal Representations of Orthogonal Lie Algebras

Abstract

By using Shen’s technique of mixed product, Xu and Zhao constructed an inhomogeneous representation on the tensor space of any finite-dimensional irreducible o(n)-module with the polynomial space, and found a sufficient condition for this representation to be irreducible. In this paper, the author gives a sufficient and necessary condition for the irreducibility of this representation. Note that the Laplace operator and partial differential operators play important roles in the proof.

Keywords

Irreducibility / Polynomial space / Laplace operator / Orthogonal Lie algebra / 17B10

References

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