# Families from SO(32)

$latex \begin{array}{llll} 496=\\ {\bf (1,24,1^c) }&+{\bf [1,15,\bar 3^c]}&+{\bf [1, \bar {15}, 3^c]}&+\\ 1,24,8^c&+[1,10,\bar 6^c]&+[1,\bar {10},6^c]&+\\ (1,1,8^c)&&&+\\&(2,5,3^c)&+(2,\bar 5,\bar 3^c)&+\\ &(1,1,1^c)&+[1,1,1^c]\\ \end{array}$

(or from SO(30), or perhaps just O(10)xU(3) or U(5)xU(3))

Point is, the first three lines seem to contain three generations with
electric and colour charge. It is possible to break the 24 and 15
from su5 to su3 + su2, and then identify the electric charge.

$latex \begin{array}{lrrcrr} & Q_1 & Q_2 & su3 + su2 & Q_3 & N \\ (1,24,1^c) &0&0& (8, 1) + (1, 3) +(1, 1)&0 & 12\\ & 0 & 0 & (3,2) & 5 & 6\\ & 0 & 0 & (\bar 3,2) & -5 &6\\ (1,15,\bar 3^c)&0&4&(\bar 6,1)&4&6\\ &0&4&(3,2)&-1&6\\ &0&4&(1,3)&-6&3\\ (1, \bar {15}, 3^c)&0&-4&\\ (1,24,8^c)&0&0&\\ (1,10,\bar 6^c)&0&4&(\bar 3,1)&4\\ &0&4&(3,2)&-1\\ &0&4&(1,1)&-6\\ (1,\bar {10},6^c)&0&-4&\\ (1,1,8^c)&0&0&\\ (2,5,3^c)&2&\pm 2&(3,1)&2\\ &2&\pm 2&(1,2)&-3\\ (2,\bar 5,\bar 3^c)&-2&\pm 2&\\ (1,1,1^c)&0&\\ (1,1,1^c)&0& \end{array}$

We can choose 4(Q2+Q3)=-2/3 and Q3=-1/5 or 4(Q2+Q3)=1/3 and Q3=1/5

Honest problem is, I do not know how to identify weak isospin, nor weak hypercharge,
given that we are looking, I guess, to scalars. Perhaps the repr is too big, doubled?

### 2 thoughts on “Families from SO(32)”

1. (496)^2 = mh/me = 4*(2Pi)^6

mh = higgs boson mass
me = electron mass

4*(2Pi)^6/7^2 ( uncertainty principle extended to d dimensions)

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