## Saturday, April 16, 2011

### Theory Update 79

Welcome to all our readers from KITP (yes, bloggers can see who visits their site). In the talk yesterday, Arkani-Hamed mentions the work of the mathematician Goncharov (welcome also to viewers from Brown University). So we see in this recent paper the introduction of the associahedra polytopes, on page 7. Goncharov is also interested in tropical geometry, which is pretty cool. On page 13 we find a special $3 \times 3$ matrix. Devadoss is not mentioned, but moduli spaces are discussed. Happy reading!

3. The extension of the symmetric group I was working on is the permutation group on three pairs. That is, the two elements of a pair stay together but can swap. This is a 6x8 = 48-element finite group and is non Abelian but otherwise is like $P_3\times P_2^3$ (which is the finite group I was using at the time of the above comment, due to a programming error).
The result was that the primitive idempotents had real parts (which I think of as weak hypercharge) with relative values of 1,2 and 3. For $P_3$ the values were 1 and 2 so this is an improvement. The actual primitive weak hypercharge relative values are 0,1,2,3,4,6, that is, 0,1/3, 2/3, 1, 4/3, and 2.