ar X iv : m at h / 04 02 41 6 v 1 [ m at h . R T ] 2 5 Fe b 20 04 DIFFERENTIAL OPERATORS AND COHOMOLOGY GROUPS ON THE BASIC AFFINE SPACE
نویسندگان
چکیده
We study the ring of differential operators D(X) on the basic affine space X = G/U of a complex semisimple group G with maximal unipo-tent subgroup U. One of the main results shows that the cohomology group H * (X, O X) decomposes as a finite direct sum of non-isomorphic simple D(X)-modules, each of which is isomorphic to a twist of O(X) by an automorphism of D(X). We also use D(X) to study the properties of D(Y) for highest weight varieties Y. For example we prove under mild hypotheses that Y is D-simple in the sense that O(Y) is a simple D(Y)-module and produce an irreducible G-module of differential operators on Y of degree −1 and specified order.
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We study the ring of differential operators D(X) on the basic affine space X = G/U of a complex semisimple group G with maximal unipotent subgroup U . One of the main results shows that the cohomology group H(X,OX) decomposes as a finite direct sum of non-isomorphic simple D(X)modules, each of which is isomorphic to a twist of O(X) by an automorphism of D(X). We also use D(X) to study the prope...
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