Finite dimensional irreducible representations of the quantum supergroup Uq(gl(m/n))
Finite dimensional irreducible representations of the quantum supergroup Uq(gl(m/n))
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DOI：
10.1063/1.530198
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发表时间：
1993-03
影响因子：
1.3
通讯作者：
Rui-bin Zhang
中科院分区：
文献类型：
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作者：
Rui-bin Zhang
在诱导模构造的框架下，系统地研究了量子超群Uq（gl（m/n））在类属q和q为单位根时的有限维不可约表示.表示论在一般q处与gl（m/n）相当相似，但当q是单位根时则截然不同。在后一种情况下，最高权不可约表示（irreps）的等价性条件被大大改变，并且这样的有限维不可约表示出现，不具有最高权和/或最低权向量。作为具体的例子，对Uq（gl（2/1））的非代表进行了分类.
Finite dimensional irreducible representations of the quantum supergroup Uq(gl(m/n)) at both generic q and q being a root of unity are investigated systematically within the framework of the induced module construction. The representation theory is rather similar to that of gl(m/n) at generic q, but drastically different when q is a root of unity. In the latter case, atypicality conditions of highest weight irreducible representations (irreps) are substantially altered, and such finite‐dimensional irreps arise that do not have highest weight and/or lowest weight vectors. As concrete examples, the irreps of Uq(gl(2/1)) are classified.