Super duality and Kazhdan-Lusztig polynomials
Super duality and Kazhdan-Lusztig polynomials
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DOI：
10.1090/s0002-9947-08-04447-4
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发表时间：
2004-09
影响因子：
1.3
通讯作者：
Shun-Jen Cheng;Weiqiang Wang;Ruibin Zhang
中科院分区：
文献类型：
--
作者：
Shun-Jen Cheng;Weiqiang Wang;Ruibin Zhang
我们建立了李代数和李超代数（A型）的表示理论之间的直接联系，通过他们的Kazhdan-Lusztig理论的Fock空间重构。因此，一般线性李超代数的有限维不可约模的特征标可由通常的A型抛物Kazhdan-Lusztig多项式计算。此外，我们还建立了任意两个A型基本表示的张量积的正则基和对偶正则基的封闭公式。
We establish a direct connection between the representation theories of Lie algebras and Lie superalgebras (of type A) via Fock space reformulations of their Kazhdan-Lusztig theories. As a consequence, the characters of finite-dimensional irreducible modules of the general linear Lie superalgebra are computed by the usual parabolic Kazhdan-Lusztig polynomials of type A. In addition, we establish closed formulas for canonical and dual canonical bases for the tensor product of any two fundamental representations of type A.