Drinfeld上半空间上的等变向量丛
Equivariant vector bundles on Drinfeld's upper half space
摘要：
设X是Q_p的有限扩张K上的d维Drinfeld上半空间，对于射影空间P^d上的齐次向量丛F，我们构造了F（X）上闭K-Frechet空间的GL_{d+1}（K）-等变滤子.这通过对偶性产生了强对偶上的局部解析GL_{d+1}（K）-表示的过滤。这个过滤的分次片是局部解析的诱导表示从局部代数的极大抛物子群。本文推广了Schneider和Teitelbaum的典范丛和Pohlkamp的结构层的情形。
英文摘要：
Let X be Drinfeld's upper half space of dimension d over a finite extension K of Q_p. We construct for every homogeneous vector bundle F on the projective space P^d a GL_{d+1}(K)-equivariant filtration by closed K-Frechet spaces on F(X). This gives rise by duality to a filtration by locally analytic GL_{d+1}(K)-representations on the strong dual. The graded pieces of this filtration are locally analytic induced representations from locally algebraic ones with respect to maximal parabolic subgroups. This paper generalizes the cases of the canonical bundle due to Schneider and Teitelbaum and that of the structure sheaf by Pohlkamp.
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