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.
| Author: | Sascha Georg Lukac |
|---|---|
| URN: | urn:nbn:de:hebis:30-45731 |
| Advisor: | Hugh Morton |
| Document Type: | Book |
| Language: | English |
| Year of Completion: | 2001 |
| Year of first Publication: | 2001 |
| Publishing Institution: | Universitätsbibliothek Johann Christian Senckenberg |
| Granting Institution: | Universität |
| Release Date: | 2007/06/22 |
| Page Number: | 192 |
| Note: | Zgl. Liverpool, Univ., Diss., 2001 |
| Source: | Liverpool, Univ., Diss., 2001 |
| HeBIS-PPN: | 189020148 |
| Institutes: | Informatik und Mathematik / Mathematik |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  Deutsches Urheberrecht |
