Resolutions for Locally Analytic Representations
Shishir Agrawal, Matthias Strauch

TL;DR
This paper develops a new resolution technique for locally analytic representations of p-adic groups by modifying existing complexes and linking them to Lie algebra cohomology, enabling computation of extension groups.
Contribution
It introduces an analytic variant of the Schneider-Stuhler complex and connects it with Chevalley-Eilenberg complexes for better analysis of locally analytic representations.
Findings
Constructed an 'analytic' Schneider-Stuhler complex for locally analytic representations.
Established a resolution linking the complex to Lie algebra cohomology.
Provided a method to compute extension groups for admissible locally analytic representations.
Abstract
The purpose of this paper is to study resolutions of locally analytic representations of a -adic reductive group . Given a locally analytic representation of , we modify the Schneider-Stuhler complex (originally defined for smooth representations) so as to give an `analytic' variant . The representations in this complex are built out of spaces of analytic vectors for compact open subgroups , indexed by facets of the Bruhat-Tits building of . These analytic representations (of compact open subgroups of ) are then resolved using the Chevalley-Eilenberg complex from the theory of Lie algebras. This gives rise to a resolution for each representation in the analytic Schneider-Stuhler complex. In a last step we show that…
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Taxonomy
TopicsNeural Networks and Applications · Advanced Control Systems Optimization · Topological and Geometric Data Analysis
