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Power sums and Homfly skein theory | | Hugh R. Morton
; | | Date: |
8 Nov 2001 | | Journal: | Geom. Topol. Monogr. 4 (2002) 235-244 | | Subject: | Geometric Topology; Quantum Algebra MSC-class: 57M25, 20C08 | math.GT math.QA | | 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}. | | Source: | arXiv, math.GT/0111101 | | Services: | Forum | Review | PDF | Favorites | |
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