| Summary: | 碩士 === 國立臺灣大學 === 數學研究所 === 93 === Ortho-symplectic Lie superalgebra osp can be realized
as differential operators and homogeneous polynomial
space is closed under its action, that is,
homogeneous polynomial space is an osp-module.
Our thesis is to study whether or not homogeneous polynomial space
can be reduced to a direct sum of irreducible osp-modules.
Our conclusion is for any odd homogeneous polynomial space,
the answer is yes. For even, the answer is no in the case
of degree 2, and therefore invalid for any even homogeneous
polynomial space since it must contain a submodule isomorphic
to degree 2 homogeneous polynomial space. However, a complete
decomposition of arbitrary even homogeneous polynomial space
has not been reached yet.
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