|
|||||
|
|
| A 类量子群和 Hecke 代数的 Schur-Weyl 对偶 | |
| 引用本文： | 蒋立宁,王正栋. A 类量子群和 Hecke 代数的 Schur-Weyl 对偶[J]. 数学进展, 2000, 29(5): 444-456 |
| 作者姓名： | 蒋立宁 王正栋 |
| 作者单位： | 北京大学数学科学学院, 北京, 100871, 中国 |
| 基金项目： | his work was supported by the NSFC |
| 摘 要： | 设Vm是量子群Uq（SLm)的标准表示，通过Hecke代数的作用，作者将Vm的张量积V^nm分解成了Uq(SLm)的不可约表示的直和，从而给出了Uq(SLm)与Hecke代数的H（q,n)Schur-Weyl对偶的完整证明，进一步得到，当q是实数时，在Hilbert空间H^n上，Uq(SL∞）和H（q,n)之间存在着Schur-Weyl对偶。 |
| 关 键 词： | SCHUR－WEYL对偶 HECKE代数 对称群 A类量子群 |
| 修稿时间： | 1998-11-13 |
The Schur-Weyl Duality Between Quantum Group of Type A and Hecke Algebra |
|
| JIANG Lining,WANG ZhengDong. The Schur-Weyl Duality Between Quantum Group of Type A and Hecke Algebra[J]. Advances in Mathematics(China), 2000, 29(5): 444-456 | |
| Authors: | JIANG Lining WANG ZhengDong |
| Abstract: | Let Vm be the standard representation of quantum group Uq(SLm).Through the action of Hecke algebra, we decompose the tensor powersVmn of Vm into the direct sum of irreducible representationsof Uq(SLm). Thus we get a complete proof of the Schur-Weyl duality between Uq(SLm) and Hecke algebra, whichis announced in ［J1］ without proof. Also when q is a real number,we have the duality between UqSL and H(q,n) on the Hilbert spaceHn. |
| Keywords: | Schur-Weyl duality quantum group Hecke algebra symmetric group |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ | |