Power sums and Homfly skein theory

2001/11/30 by Hugh R. Morton
Mathematics · #math.GT #math.QA #msc:57M25 #msc:20C08

paper · pdf

published as Geom. Topol. Monogr. 4 (2002) 235-244 · Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon4/paper15.abs.html

arxiv created 2002/10/20 · arxiv updated 2009/11/30

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.

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