 Representations of SO(4) from two SU2 spins

ID: representations-of-so-4-from-two-su2-spins

V_{j_{L}} \otimes V_{j_{R}}

give the irreducible representations of the Spin(4) double cover. The simultaneous central sign acts by

(- 1)^{2 j_{L} + 2 j_{R}}

, so exactly the integer-sum pairs descend to SO(4). Their dimensions are

(2 j_{L} + 1) (2 j_{R} + 1)

∣ j_{L} - j_{R} ∣

through

j_{L} + j_{R}

in steps of one.

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