Symmetric Tensors in Ortho-symplectic Lie Superalgebra of Dimension (4,4)

• Main Authors: CHIEN-YI MA, 馬鑑一
• Other Authors: 程舜仁
• Format: Others
• Language: en_US
• Published: 2005
• Online Access: http://ndltd.ncl.edu.tw/handle/43066528074507216240

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.