User ross elliot - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T03:54:58Z http://mathoverflow.net/feeds/user/20812 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/123152/exceptional-schur-weyl-duality Exceptional Schur-Weyl Duality Ross Elliot 2013-02-27T21:57:01Z 2013-02-27T23:33:41Z <p>Are there any known analogs of Schur-Weyl duality for the exceptional groups?</p> <p>In particular, I am looking to decompose the tensor powers of the action of \$E_6\$ on its 27-dimensional module. Any advice or references to this end would be greatly appreciated.</p> http://mathoverflow.net/questions/86404/quantum-e6-e7-knot-polynomials Quantum E6/E7 knot polynomials Ross Elliot 2012-01-22T21:38:33Z 2012-03-11T15:41:58Z <p>Has anybody seen seen quantum knot invariants associated to (E6, 27) or (E7, 56) worked out in the literature? Even for just simple knots like the trefoil or figure-8?</p> <p>I suspect these haven't been worked out, but if anybody knows of a reference containing these or even just discussing them, please let me know.</p> http://mathoverflow.net/questions/109328/pair-of-pants-coordinates-in-s3-times-mathbbr Comment by Ross Elliot Ross Elliot 2012-10-10T20:26:48Z 2012-10-10T20:26:48Z Apologies for the confusion. By &quot;pair of pants cobordism&quot; I mean a thrice-punctured \$S^2\$ interpreted as a cobordism from the unknot to the unlink of two components (or vice versa). The messy polynomial can be seen to give such a surface by considering the corresponding homotopy \$f_t\$. http://mathoverflow.net/questions/86404/quantum-e6-e7-knot-polynomials Comment by Ross Elliot Ross Elliot 2012-01-22T22:38:06Z 2012-01-22T22:38:06Z 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.