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Power sums and Homfly skein theory

Hugh R Morton

Geometry & Topology Monographs 4 (2002) 235–244

DOI: 10.2140/gtm.2002.4.235

Abstract

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.

Keywords

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

Mathematical Subject Classification

Primary: 57M25

Secondary: 20C08

References
Publication

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

Authors
Hugh R Morton
Department of Mathematical Sciences
University of Liverpool
Peach St
Liverpool
L69 7ZL
UK
http://www.liv.ac.uk/~su14/