科研之友
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摘要
Let G be a locally semisimple ind-group, P be a parabolic subgroup, and E be a finite-dimensional P-module. We show that, under a certain condition on E, the nonzero cohomologies of the homogeneous vector bundle O-G/p(E*) on G/P induced by the dual P-module E* decompose as direct sums of cohomologies of bundles of the form O-G/p(R) for (some) simple constituents R of E*. In the finite-dimensional case, this result is a consequence of the Bott Borel Weil theorem and Weyl's semisimplicity theorem. In the infinite-dimensional setting we consider, there is no relevant semisimplicity theorem. Instead, our results are based on the injectivity of the cohomologies of the bundles O-G/p(R).
- 出版日期2017
