Quasi-finite modules for lie superalgebras of infinite rank
Quasi-finite modules for lie superalgebras of infinite rank
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DOI：
10.1090/s0002-9947-05-03795-5
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发表时间：
2005-07
影响因子：
1.3
通讯作者：
N. Lam;Rui-bin Zhang
中科院分区：
文献类型：
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作者：
N. Lam;Rui-bin Zhang
我们对无限秩李超代数 gl∞ | 上的准有限不可约最高权重模块进行分类∞、& 和 D，并确定此类模可单位化的充要条件。单位化的不可约模是根据自由量子场的福克空间构造的，并且通过研究无限秩李超代数和经典李群之间的豪对偶性也获得了其形式特征的显式公式。
We classify the quasi-finite irreducible highest weight modules over the infinite rank Lie superalgebras gl∞ | ∞, & and D, and determine the necessary and sufficient conditions for such modules to be unitarizable. The unitarizable irreducible modules are constructed in terms of Fock spaces of free quantum fields, and explicit formulae for their formal characters are also obtained by investigating Howe dualities between the infinite rank Lie superalgebras and classical Lie groups.