Timeline for Quantum E6/E7 knot polynomials
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Feb 29, 2012 at 12:20 | answer | added | Hauke Reddmann | timeline score: 0 | |
| Jan 24, 2012 at 8:42 | answer | added | B. Patureau | timeline score: 5 | |
| Jan 23, 2012 at 16:59 | comment | added | Noah Snyder | My recollection from conversations with Scott is that the main obstacle is that arithmetic with rational functions is slow. For the 3-strand braid group you're already talking about composing matrices that are roughly 20,000 by 20,000. | |
| Jan 23, 2012 at 10:01 | comment | added | Adrien | There is also a GAP package called Quagroup which for the quantized envelopping algebra of any simple Lie algebra can construct its highest weight modules and compute explicitely the corresponding image of the $R$ matrix. In fact it can even compute the isomorphism $V\otimes W \rightarrow W\otimes V$ for different modules $V,W$. science.unitn.it/~degraaf/quaman.html | |
| Jan 23, 2012 at 6:59 | comment | added | Bruce Westbury | I would write down the representations of the braid group directly. | |
| Jan 23, 2012 at 5:14 | history | edited | Daniel Moskovich |
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| Jan 23, 2012 at 0:15 | comment | added | Noah Snyder | Ok, my bad. I'd used it for some more basic quantum En calculations before, but I guess they were all a lot simpler than what you need. | |
| Jan 22, 2012 at 22:38 | comment | added | Ross Elliot | I spoke to Scott a couple of days ago. His package cannot compute quantum invariants for F4 or En due to the complexity of some intermediate computations. He noted that one could avoid these issues by, e.g. writing down the quantum positive roots in terms of the PBW bases... working this out is [currently] a bit beyond my primitive background in QA. However, if anybody knows of a good source for such things, that would be equally useful. | |
| Jan 22, 2012 at 22:17 | comment | added | Noah Snyder | I'm pretty sure that the quantum groups Mathematica package which is part of the Knot Atlas package (katlas.org/wiki/Main_Page) can do this. It'll probably be pretty slow. You can ask Scott Morrison if you want more info. | |
| Jan 22, 2012 at 22:17 | comment | added | Bruce Westbury | It is certainly possible to evaluate these for links which can be obtained as the closure of a braid with at most three strings. | |
| Jan 22, 2012 at 21:38 | history | asked | Ross Elliot | CC BY-SA 3.0 |