Power sums and Homfly skein theory



Morton, Hugh R ORCID: 0000-0002-8524-2695
(2001) Power sums and Homfly skein theory. Geom. Topol. Monogr., 4. pp. 235-244.

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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}.

Item Type: Article
Additional Information: Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon4/paper15.abs.html
Uncontrolled Keywords: math.GT, math.GT, math.QA, 57M25, 20C08
Depositing User: Symplectic Admin
Date Deposited: 12 Apr 2016 14:29
Last Modified: 17 Dec 2022 01:14
DOI: 10.2140/gtm.2002.4.235
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3000253