Zusammenfassung für den Vortrag am 17.01.2007 (16:00 Uhr)

Oberseminar MATHEMATISCHE PHYSIK

Bertfried Fauser (MPI MIS, Leipzig)

Knot invariants derived from character theory

Knot invariants play a central role at various places in mathematics and physics. Furthermore, the classification of knots is still an open mathematical problem. Therefore new approaches to knot invariants are always desirable. We develop knot invariants from the character Hopf algebras of centralizer subgroups of the GL(n) groups in the stable limit formula9. This invariants are induced by plethystic branchings. Usually one exploits the homomorphisms formula11 or formula13 to derive e.g. the Jones polynomial. Our method draws invariants directly from the character rings of infinitely many centralizer subgroups of formula15 and does not need mandatorily a q-deformation. We show how state models can be derived from our method and how it related for example to the Kauffman bracket and Jones polynomial. Joint work with: Peter D. Jarvis, Hobart, and Ronald C. King, Southampton.

 

06.06.2018, 07:19