18 A. W. KNAPP
is exact. But
Hom1(U(q), (t\mu)* 0 V)
Hom1(U(u) 0 U(l), (t\mu)* 0 V)
Hom1(U(l), Homc(U(u), (t\mu)* 0 V))
Hornc(U(u), (t\mu)* 0 V)
Hornc(U(u) 0
Hornc(Xm, V),
is the Koszul (projective) resolution of C in C(u, 1). (See [9, Theorem
is easy to check that the differentials for (5.13) are the ones induced from
the differentials for
and hence (5.13) is exact. This completes the proof.
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