Homfly skeins and the Hopf link

  • This thesis exhibits skeins based on the Homfly polynomial and their relations to Schur functions. The closures of skein-theoretic idempotents of the Hecke algebra are shown to be specializations of Schur functions. This result is applied to the calculation of the Homfly polynomial of the decorated Hopf link. A closed formula for these Homfly polynomials is given. Furthermore, the specialization of the variables to roots of unity is considered. The techniques are skein theory on the one side, and the theory of symmetric functions in the formulation of Schur functions on the other side. Many previously known results have been proved here by only using skein theory and without using knowledge about quantum groups.

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Author:Sascha Georg Lukac
Advisor:Hugh Morton
Document Type:Book
Year of Completion:2001
Year of first Publication:2001
Publishing Institution:Universit├Ątsbibliothek Johann Christian Senckenberg
Granting Institution:Universit├Ąt
Release Date:2007/06/22
Page Number:192
Zgl. Liverpool, Univ., Diss., 2001
Source:Liverpool, Univ., Diss., 2001
Institutes:Informatik und Mathematik / Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):License LogoDeutsches Urheberrecht