On irreducible representations of compact \(p\)-adic analytic groups (Q363349)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On irreducible representations of compact \(p\)-adic analytic groups |
scientific article; zbMATH DE number 6203673
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On irreducible representations of compact \(p\)-adic analytic groups |
scientific article; zbMATH DE number 6203673 |
Statements
On irreducible representations of compact \(p\)-adic analytic groups (English)
0 references
2 September 2013
0 references
The authors prove that the canonical dimension of a coadmissible representation of a semisimple \(p\)-adic Lie group in a \(p\)-adic Banach space is either zero or at least half the dimension of a nonzero coadjoint orbit. To do this, they establish analogues for \(p\)-adically completed enveloping algebras of Bernstein's inequality for modules over Weyl algebras, the Beilinson-Bernstein localisation theorem, and Quillen's lemma about the endomorphism ring of a simple module over an enveloping algebra.
0 references
\(p\)-adic Banach space representations
0 references
\(\mathcal{D}\)-modules
0 references
affinoid algebras
0 references
Beilinson-Bernstein localisation
0 references
central characters
0 references
0 references
