## Dimensions of $E_{7\frac{1}{2}}$

Is there much known about the dimensions $$D$$ of $$E_{7\frac{1}{2}}$$ ($$D_6.H_{32}$$) beyond $$44\bigotimes44(def)=1\bigoplus945\bigoplus99(adj)\bigoplus891$$? 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: $$E_7,m=8,C=54,D_1=365750,D_2=0;C_3,m=1,C=12,D_1=525,D_2=385$$). 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 🙂