Abstract
This chapter presents homogeneous line bundle L corresponding to the representation in unitary degenerate series with the most singular parameter. A holomorphic homogeneous line bundle is obtained on Gc/Pc whose restriction to G/P is L. This line bundle is denoted and the sheaf of its holomorphic sections by the same letter L. Some relation are investigated between the Cech cohomology group H2 (▪, L) and a decomposition of the degenerate series representation in Kashiwara and Vergne. Although the K-type of this cohomology group is known by the very general result of Rawnsley, Schmid, and Wolf, the approach is purely geometric and an injective G-equivariant boundary map is constructed of the cohomology space to the space of hyperfunction-section of L on G/P using a Mayer–Vietris exact sequence.
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