Volume 4 (2002)

Download this article
For screen
For printing
Recent Volumes
Volume 1, 1998
Volume 2, 1999
Volume 3, 2000
Volume 4, 2002
Volume 5, 2002
Volume 6, 2003
Volume 7, 2004
Volume 8, 2006
Volume 9, 2006
Volume 10, 2007
Volume 11, 2007
Volume 12, 2007
Volume 13, 2008
Volume 14, 2008
Volume 15, 2008
Volume 16, 2009
Volume 17, 2011
Volume 18, 2012
Volume 19, 2015
The Series
All Volumes
About this Series
Ethics Statement
Purchase Printed Copies
Author Index
ISSN (electronic): 1464-8997
ISSN (print): 1464-8989
MSP Books and Monographs
Other MSP Publications

Power sums and Homfly skein theory

Hugh R Morton

Geometry & Topology Monographs 4 (2002) 235–244

DOI: 10.2140/gtm.2002.4.235


The Murphy operators in the Hecke algebra Hn of type A are explicit commuting elements, whose symmetric functions are central in Hn. 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 Hn, and found an element Pm in C, independent of n, whose image, up to an explicit linear combination with the identity of Hn, is the mth power sum of the Murphy operators. The aim of this paper is to give simple geometric representatives for the elements Pm, and to discuss their role in a similar construction for central elements of an extended family of algebras Hn,p.


HOMFLY skein theory, Murphy operators, power sums, supersymmetric polynomials, annulus, Hecke algebras

Mathematical Subject Classification

Primary: 57M25

Secondary: 20C08


Received: 31 October 2001
Revised: 15 May 2002
Accepted: 22 July 2002
Published: 13 October 2002

Hugh R Morton
Department of Mathematical Sciences
University of Liverpool
Peach St
L69 7ZL