Drinfeld对称空间的上同调与调和上链
Cohomology of Drinfeld symmetric spaces and Harmonic cochains
摘要：
设K是非阿基米德局部域。本文给出了GL_{n+1}（K）特殊表示的对偶与定义在GL_{n+1}（K）的Bruhat-Tits构造上的调和上链空间之间的显式同构，调和上链的定义是E. de Shalit [建筑物上的剩余和p-adic对称域的de Rham上同调，Duke Math. J.，106，123-191，（2000）]。我们应用P. Schneider和U. Stuhler，[P-adic对称空间的上同调，Inv. Math.105，47-122，（1991）]，对任意特征的K，在Drinfeld对称空间的上同调群与调和上链空间之间存在GL_{n+1}（K）-等变同构.
英文摘要：
Let K be a non-archimedean local field. This paper gives an explicit isomorphism between the dual of the special representation of GL_{n+1}(K)$and the space of harmonic cochains defined on the Bruhat-Tits building of GL_{n+1}(K), the definition of harmonic cochains is in the sense of E. de Shalit [Residues on buildings and de Rham cohomology of p-adic symmetric domains, Duke Math. J., 106, 123-191, (2000)]. We deduce, applying a work of P. Schneider and U. Stuhler, [The cohomology of p-adic symmetric spaces, Inv. Math. 105, 47-122, (1991)], that for K of any characteristic, there exists a GL_{n+1}(K)-equivariant isomorphism between the cohomology group of the Drinfeld symmetric space and the space of harmonic cochains.
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