Is there much known about the dimensions $D$ of $E_{7\frac{1}{2}}$ (that is: $D_6.H_{32}$) beyond $$ 44\otimes44(def)=1\oplus945\oplus99(adj)\oplus891\, ? $$ Generally, does a weight indexing scheme like for the semisimple $E_7$ cousins exist? Particularly, is $D=134805$ an irrep dimension or the sum of two $D_1+D_2$?
Background: In the $E_7$ series, in $def^{\bigotimes4}$ there always pops up a pair of dimensions with equal quadratic Casimir ($C=6(m+1)$, your gauge may vary, I conform to the Hayashi paper on quantum dimensions) but in most cases one partner will be identically zero (one example for each case: $E_7$: $m=8,C=54, D_1=365750,D_2=0$, and $C_3$: $m=1,C=12,D_1=525,D_2=385$). And my "magic" formulae only give the sum.
P.S. In case nothing is known and anyone needs a few dimensions $D$ of $E_{7\frac{1}{2}}$ together with the quadratic Casimirs and the Clebsch–Gordan series, just ask; what I do is not math but it works :-)