G.2 Subduction
237
G.2 Subduction
SO(3)I
O
j
1/2
E 1/2
E 1/2
3/2
G 3/2
G 3/2
5/2
I 5/2
E 5/2 + G 3/2
7/2
E 7/2 + I 5/2
E 1/2 + E 5/2 + G 3/2
9/2
G 3/2 + I 5/2
E 1/2 + 2G 3/2
11/2
E 1/2 + G 3/2 + I 5/2
E 1/2 + E 5/2 + 2G 3/2
13/2
E 1/2 + E 7/2 + G 3/2 + I 5/2
E 1/2 + 2E 5/2 + 2G 3/2
15/2
G 3/2 + 2I 5/2
E 1/2 + E 5/2 + 3G 3/2
17/2
E 7/2 + G 3/2 + 2I 5/2
2E 1/2 + E 5/2 + 3G 3/2
19/2
E 1/2 + E 7/2 + G 3/2 + 2I 5/2
2E 1/2 + 2E 5/2 + 3G 3/2
G.3 Canonical-Basis Relationships
D ∗
3
D(C
z
3 )
D(C x
2 )
|E 1/2 α, |E 1/2 β
1−i
√
3
2
0
0
1+i
√
3
2
0 −i
−i 0
|E 3/2 ρ 1
(−1)( i )
|E 3/2 ρ 2
(−1)( −i)
D ∗
4
D(C
z
4 )
D(C x
2 )
|E 1/2 α, |E 1/2 β
1−i √
2
0
0
1+i √
2
0 −i
−i 0
|E 3/2 α ′ , |E 3/2 β ′
−1+i √
2
0
0
−1−i √
2
0 −i
−i 0
The components of the fourfold-degenerate G 3/2 irrep in O ∗ and I ∗ are labeled as κ, λ, μ, and ν. For a quartet spin, these labels correspond to M S =
+3/2, +1/2, −1/2, and −3/2, respectively.
O ∗
D(C
z
4 )
D(C
xyz
3 )
|E 1/2 α, |E 1/2 β
1
√
2
1 − i
0
01 + i
1−i
2
−1−i
2
1−i
2
1+i
2
|E 5/2 α ′ , |E 5/2 β ′
1
√
2
−1 + i
0
0
−1 − i
1−i
2
−1−i
2
1−i
2
1+i
2