We give the complete proof of the Adams E2-term for the complex connective K-theory of Ω(SU(n)/SO(n)) for n = 2, 3, and 4.

1.Introduction ...............1
2.Proof of Theorem 1 .........3
3.Proof of Theorem 2 .........8
4.Proof of Theorem 3 ........14
5.References ................17

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