Power sums and Homfly skein theory

Details Power sums and Homfly skein theory Power sums and Homfly skein theory

2001-11-08

arxiv.org/abs/math/0111101v3

Geom. Topol. Monogr. 4 (2002) 235-244

Mathematics

Geometric Topology

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

Scientific paper

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}.

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