English

Power sums and Homfly skein theory

Geometric Topology 2007-05-23 v3 Quantum Algebra

Abstract

The Murphy operators in the Hecke algebra H_n of type A are explicit commuting elements, whose symmetric functions are central in H_n. In [Skein theory and the Murphy operators, J. Knot Theory Ramif. 11 (2002), 475-492] I defined geometrically a homomorphism from the Homfly skein C of the annulus to the centre of each algebra H_n, and found an element P_m in C, independent of n, whose image, up to an explicit linear combination with the identity of H_n, is the m-th power sum of the Murphy operators. The aim of this paper is to give simple geometric representatives for the elements P_m, and to discuss their role in a similar construction for central elements of an extended family of algebras H_{n,p}.

Keywords

Cite

@article{arxiv.math/0111101,
  title  = {Power sums and Homfly skein theory},
  author = {Hugh R. Morton},
  journal= {arXiv preprint arXiv:math/0111101},
  year   = {2007}
}

Comments

Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon4/paper15.abs.html