Timeline for Degree 8 multilinear operations on Jordan algebras
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 25, 2023 at 16:06 | comment | added | John Wiltshire-Gordon | I sent you an email, so let me know if you didn't get it. | |
| Feb 25, 2023 at 14:57 | comment | added | Vladimir Dotsenko | I see. Thank you for the explanation. Altogether implementing this from scratch is probably beyond my personal programming skills. Do you happen to know of any people who did implement similar things in the past? | |
| Feb 25, 2023 at 14:00 | comment | added | John Wiltshire-Gordon | Do not expand these hidden rows into the matrix. Just leave the entries of the matrix as strings that can be parsed into the group algebra. If we do expand in the way that you say, then it's like tensoring with the regular representation. My suggestion is to tensor with each irrep in turn. | |
| Feb 25, 2023 at 8:47 | comment | added | Vladimir Dotsenko | Indeed, you are choosing to fill the matrix with elements of $\mathbb{Q}S_8$, so my second concern does not literally apply. But just because you decided to "hide" the large number in the elements of the matrix, does not change the fact that the presentation matrix is an element of a vector space whose dimension is in hundreds of thousands or rather millions, as far as the first step is concerned. | |
| Feb 25, 2023 at 3:25 | comment | added | John Wiltshire-Gordon | 1) I see that you are correct and I'm missing some generators coming from pre and post multiplication 2) I'm using the action of S_8 to hit all relabelings of the each tree, so I think the second point is not correct. | |
| Feb 24, 2023 at 23:55 | comment | added | Vladimir Dotsenko | Also, and probably much more importantly, the binary trees have labelled leaves, so the number of binary trees with 8 leaves is (oeis.org/A001147) equal to 13!!=135135 - much more than 429. So I fear that the approach you suggest is highly unlikely to help. | |
| Feb 24, 2023 at 21:11 | comment | added | Vladimir Dotsenko | Dear John, alas the presentation you write is not enough, these are not all consequences. For example, there are consequences of the identity $F(a_1,a_2,a_3,a_4)$ of the form $a_1F(a_2,T_3,T_4,T_5)$, where $T_3$, $T_4$, $T_5$ are some trees, etc. In other words, you can precompose and postcompose with something. So the computation is much bigger. | |
| Feb 24, 2023 at 20:59 | history | answered | John Wiltshire-Gordon | CC BY-SA 4.0 |