SO(5)⊃SO(3) reduced state labels

The seniority v representation of SO(5) contains the SO(3) irrep of angular momentum L with a multiplicity d_v,L given by

d_v,L= (⌊(v-b)/3⌋+1)θ_v-b -⌊(v-L+2)/3⌋θ_v-L+2,

where b=L/2 for L even, and b=(L+3)/2 for L odd, and we define θ_k=1 for k≥0, and θ_k=0 for k<0.

For 0≤v≤50, the links 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, lists the labels v:L;α for all states with a fixed seniority v. In those cases where v and L uniquely specify the vector, the label α has been omitted.