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Published in:
2017 | OriginalPaper | Chapter
13. Oscillator Representations of gl(n|m) and \({ osp}(n|2m)\)
Author : Xiaoping Xu
Published in: Representations of Lie Algebras and Partial Differential Equations
Publisher: Springer Singapore
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Abstract
We first establish two-parameter \(\mathbb {Z}^2\)-graded supersymmetric oscillator generalizations of the classical theorem on harmonic polynomials for the general linear Lie superalgebra. Then we extend the result to two-parameter \(\mathbb {Z}\)-graded supersymmetric oscillator generalizations of the classical theorem on harmonic polynomials for the ortho-symplectic Lie superalgebras.