2020
DOI: 10.48550/arxiv.2012.07402
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Invertible analytic functions on Drinfeld symmetric spaces and universal extensions of Steinberg representations

Abstract: Recently, Gekeler proved that the group of invertible analytic functions modulo constant functions on Drinfeld's upper half space is isomorphic to the dual of an integral generalized Steinberg representation. In this note we show that the group of invertible functions is the dual of a universal extension of that Steinberg representation. As an application, we show that lifting obstructions of rigid analytic theta cocycles of Hilbert modular forms in the sense of Darmon-Vonk can be computed in terms of L-invari… Show more

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