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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeMay 6th 2021
• (edited May 6th 2021)

With David Corfield and Hisham Sati we are finalizing an article:

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The title refers to a proof presented, that all fundamental gl(n)-weight systems on horizontal chord diagrams are states with respect to the star-involution of reversion of strands.

But the bulk of the article rephrases this theorem and its proof as a special case of a more general statement in geometric group theory: characterizing the (non/semi-)positive definite phases of the Cayley distance kernel on the symmetric group.

Finally, a last section recalls from Sati, Schreiber 2019c the original motivation and interpretation of this result: Under Hypothesis H it proves, from first principles, that a pair of coincident M5-branes (transversal on a pp-wave background, as in the BMN matrix model) indeed do form a (bound) state. This is of course generally expected, but there did not use to be a theory to derive this from first principles.

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• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeMay 7th 2021

This just made it into Dror Bar-Natan’s Pensieve:

• CommentRowNumber3.
• CommentAuthorDavid_Corfield
• CommentTimeMay 17th 2021

Example 3.11

• should be $\lambda_{rows(\lambda)}$ at end of first bracket
• in 1), should be “labels to fill its first column”
• in 2) should be “any labelling of the first column”
• CommentRowNumber4.
• CommentAuthorDavid_Corfield
• CommentTimeMay 17th 2021
• (edited May 17th 2021)

respectivey

We close with briefly explaining

’by’ sounds better than ’with’

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeMay 18th 2021

Thanks, fixed now locally. I’ll upload after adding a pointer to Jucys’ theorem which we have re-derived…