# Finding the Hilbert expansion of a D4 Coulomb branch

I am trying to compute the HS of the following Coulomb branch, but first I am not sure how to proceed in interpreting the diagram and what variables to use. I am trying to use the equation from this paper Monopole operators and Hilbert series of Coulomb branches of 3d ${\cal N} = 4$ gauge theories. Any help or hint will be appreciated.

• That would be the gauge theory from part 3.4 of the paper? And the Young tableau is explained in Appendix A? – Mitchell Porter Mar 1 '17 at 4:49
• @MitchellPorter In order to obtain the Young tables the values of the magnetic flux are needed, so what are they for this diagram? – James J Mar 5 '17 at 16:18
• Do you need to know specific values? Or just multiplicities? - "how many of the fluxes... are equal" – Mitchell Porter Mar 14 '17 at 18:35