Schur–Weyl Reciprocity between the Quantum Superalgebra and the Iwahori–Hecke Algebra
Schur–Weyl Reciprocity between the Quantum Superalgebra and the Iwahori–Hecke Algebra
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DOI：
10.1007/s10468-006-9014-5
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发表时间：
2005-06
影响因子：
0.6
通讯作者：
H. Mitsuhashi
中科院分区：
文献类型：
--
作者：
H. Mitsuhashi
本文建立了量子广义超李代数U_q^\sigma\big{（}{\mathfrak{g}\mathfrak{l}}（m，n）\big{）}$与Iwahori-Hecke代数之间的Schur-Weyl互易性.本文在分维向量空间的张量空间上引入了的符号置换表示。这个作用量与上的向量表示导出的$U_q^\sigma\big{（}{\mathfrak{g}\mathfrak{l}}（m，n）\big{）}$的作用量可交换，这两个子代数满足Schur-Weyl互易性.作为特例，我们得到了超情形（）和量子情形（）。因此，这个结果包括了超情形和量子情形，并且统一了这两种重要的情形。
In this paper, we establish Schur–Weyl reciprocity between the quantum general super Lie algebra $U_q^\sigma\big{(}{\mathfrak{g}\mathfrak{l}}(m,n)\big{)}$ and the Iwahori–Hecke algebra. We introduce the sign-permutation representation ofon the tensor spaceofdimensional-graded-vector space. This action commutes with that of $U_q^\sigma\big{(}{\mathfrak{g}\mathfrak{l}}(m,n)\big{)}$ derived from the vector representation on. Those two subalgebras ofsatisfy Schur–Weyl reciprocity. As special cases, we obtain the super case (), and the quantum case (). Hence this result includes both the super case and the quantum case, and unifies those two important cases.