Geometry & Topology Monographs 4 (2002) 235–244

DOI: 10.2140/gtm.2002.4.235

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 mth 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.

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