Differential Operators and Cohomology Groups on the Basic Affine Space
نویسنده
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 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 properties of D(Z) for highest weight varieties Z. For example, we prove that Z is D-simple in the sense that O(Z) is a simple D(Z)-module and produce an irreducible G-module of differential operators on Z of degree −1 and specified order.
منابع مشابه
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