By James B. Carrell
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SL(2,JD) c G by the The maximal torus in this 02* action of Theorem 7 where can be viewed as an analytic ring. k = 2. Its relations will be reflected in the structure of an infinitesimal neighborhood of the zero. e. the closures of the Bruhat cells, admit an intrinsic characterization in the ring duals of these classes in explicitly in CBGG] . H (G/B,0Z) . The Poincare H* (G/B,ID) are calculated We will return to this question in §9. 8. A REMARK ON RATIONALITY The condition of Theorem 7 that vector field V some integer k / 0 X-^CtJ-X" 1 k = 4>(X t) $ : E •* Aut(X) Aut(X) and a X admit a holomorphic 02* action so that dX-V = XV for is equivalent to requiring "that for all X e 02* , t e 0] , where is the one parameter subgroup (of the group of automorphisms of X ) generated by V .
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Laksov, Schubert Calculus, Am. Math Monthly 79 (1972), 1061-1082. ~ CKob] S. Kobayashi, Trans formation groups in differential geometry, Springer- Ver lag, New York Tl972) . CKon] J. Konarski, Properties of projective orbits of actions of affine algebraic groups, to appear. CKos] B. Kostant, Lie group representations on polynomial rings, Amer. J. of Math. 8£, 327-404. I. Lieberman, Rationality and holomorphic vector fields, to. appear. _ Holomorphic vector fields on projective varieties, Proc. Symp.