Power sums and Homfly skein theory

Hugh R. Morton

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Power sums and Homfly skein theory

Hugh R. Morton

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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}.

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Hugh R. Morton. 2002-10-20. Power sums and Homfly skein theory. https://arxiv.org/abs/math/0111101

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