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On locally analytic Beilinson-Bernstein localization and the canonical dimension
Representation Theory · Submitted 7 Aug 2011
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In the first part of the paper we prove, under certain assumptions on G and the prime p, a localization theorem of Beilinson-Bernstein type for admissible locally analytic representations of principal congruence subgroups in the rational points of G.
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The abstract, sentence by sentence
Let G be a connected split reductive group over a p-adic field. In the first part of the paper we prove, under certain assumptions on G and the prime p, a localization theorem of Beilinson-Bernstein type for admissible locally analytic representations of principal congruence subgroups in the rational points of G. In doing so we take up and extend some recent methods and results of Ardakov-Wadsley on completed universal enveloping algebras to a locally analytic setting. As an application we prove, in the second part of the paper, a locally analytic version of Smith's theorem on the canonical dimension. This paper is in final form, is an expanded version of the former preprint 'On the dimension of locally analytic representations of semisimple p-adic groups' and has appeared in Mathematische Zeitschrift.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Let G be a connected split reductive group over a p-adic field. | background 1.00 | 0.07 | 0.02 | asserted 0.90 |
| s1 | In the first part of the paper we prove, under certain assumptions on G and the prime p, a localization theorem of Beilinson-Bernstein type for admissible locally analytic representations of principal congruence subgroups in the rational points of G. | result 0.59 | 0.96 | 0.56 | asserted 1.00 |
| s2 | In doing so we take up and extend some recent methods and results of Ardakov-Wadsley on completed universal enveloping algebras to a locally analytic setting. | method 0.95 | 0.79 | 0.04 | asserted 0.98 |
| s3 | As an application we prove, in the second part of the paper, a locally analytic version of Smith's theorem on the canonical dimension. | result 0.92 | 0.94 | 0.34 | asserted 1.00 |
| s4 | This paper is in final form, is an expanded version of the former preprint 'On the dimension of locally analytic representations of semisimple p-adic groups' and has appeared in Mathematische Zeitschrift. | background 0.97 | 0.24 | 0.02 | asserted 1.00 |
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Original abstract
Let G be a connected split reductive group over a p-adic field. In the first part of the paper we prove, under certain assumptions on G and the prime p, a localization theorem of Beilinson-Bernstein type for admissible locally analytic representations of principal congruence subgroups in the rational points of G. In doing so we take up and extend some recent methods and results of Ardakov-Wadsley on completed universal enveloping algebras to a locally analytic setting. As an application we prove, in the second part of the paper, a locally analytic version of Smith's theorem on the canonical dimension. This paper is in final form, is an expanded version of the former preprint 'On the dimension of locally analytic representations of semisimple p-adic groups' and has appeared in Mathematische Zeitschrift.
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What it cites · 18 sentences without a confident label
Builds on 1 paper
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In doing so we take up and extend some recent methods and results of Ardakov-Wadsley on completed universal enveloping algebras ( [ref] ) to a locally analytic setting.
On irreducible representations of compact $p$-adic analytic groups · Introduction · 0.98
Uses the method or tool of 1 paper
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Using these inputs the argumentation in [ref] , 6.9/10 goes through.
On irreducible representations of compact $p$-adic analytic groups · Deformations and completions · 0.81
Cites as support 1 paper
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It follows from [ref] , Lemma 6.5 that the algebra of sections $(U)$ over an open set $U∈$ equals the $p$-adic completion of $(U)$.
On irreducible representations of compact $p$-adic analytic groups · Deformations and completions · 0.99
Cites as background 1 paper
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We recall some notions and constructions related to differential operators on homogeneous spaces ( [ref] , [ref] , [ref] ) thereby fixing some notation.
On irreducible representations of compact $p$-adic analytic groups · Differential operators on homogeneous spaces · 1.00
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