Skein theory and the Murphy operators
摘要
The Murphy operators in the Hecke algebra H_n of type A are explicit commuting elements whose sum generates the centre. They can be represented by simple tangles in the Homfly skein theory version of H_n. In this paper I present a single tangle which represents their sum, and which is obviously central. As a consequence it is possible to identify a natural basis for the Homfly skein of the annulus, C. Symmetric functions of the Murphy operators are also central in H_n. I define geometrically a homomorphism from C to the centre of each algebra H_n, and find an element in C, independent of n, whose image is the m-th power sum of the Murphy operators. Generating function techniques are used to describe images of other elements of C in terms of the Murphy operators, and to demonstrate relations among other natural skein elements.
引用
@article{arxiv.math/0102098,
title = {Skein theory and the Murphy operators},
author = {Hugh R. Morton},
journal= {arXiv preprint arXiv:math/0102098},
year = {2016}
}
备注
22 pages, 34 interspersed figures. Submitted for the proceedings of Knot 2000 conference, Korea