Inner products on the Hecke algebra of the braid group

被引：1

作者：

Kalman, Tamas ^{[1
]}

机构：

[1] Tokyo Inst Technol, Meguro Ku, Tokyo 1528551, Japan

来源：

TOPOLOGY AND ITS APPLICATIONS | 2011年 / 158卷 / 05期

基金：

日本学术振兴会;

关键词：

Homfly polynomial; Braids; Braid index; Hecke algebra;

D O I：

10.1016/j.topol.2010.12.014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We claim that the Homily polynomial (that is to say, Ocneanu's trace functional) contains two polynomial-valued inner products on the Hecke algebra representation of Artin's braid group. These bear a close connection to the Morton-Franks-Williams inequality. With respect to these structures, the set of positive, respectively negative permutation braids becomes an orthonormal basis. In the second case, many inner products can be geometrically interpreted through Legendrian fronts and rulings. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：643 / 646

页数：4

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