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Does anybody know whether the following irreducible representations of SU(2) are unitary?
g belongs to SU(2)
[tex][U_j(g) f](v) = f(g^{-1} v)[/tex]
f is an order-2j homogeneous complex polynomial of two complex variables v = (x, y)
e.g. for [tex]j = 1[/tex], [tex]f = 2x^2 + 3xy + 4y^2[/tex]
g belongs to SU(2)
[tex][U_j(g) f](v) = f(g^{-1} v)[/tex]
f is an order-2j homogeneous complex polynomial of two complex variables v = (x, y)
e.g. for [tex]j = 1[/tex], [tex]f = 2x^2 + 3xy + 4y^2[/tex]