On irreducible representations of compact $p$-adic analytic groups
By K. Ardakov, S. Wadsley. 2011
70 citations recorded by the source corpus.
We 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 non-zero coadjoint orbit. To do this we 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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/b6b03ab7999cd78b745e4a9d08c68e0e172fa4b3
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- The p-adic local Langlands correspondence for GL_2(Q_p) (2013, methodology): “• Schur’s lemma for unitary Banach representations of p-adic Lie groups ([27] which uses results of Ardakov and Wadsley [1].”
- Non-Archimedean analytic geometry as relative algebraic geometry (2013, methodology): “e provable in our framework. We plan to prove a version of the BeilinsonBernstein localization theorem over certain non-Archimedean fields in our context which would be a generalisation of the work of [1] over Qp. Finally, we believe that when working over a finite field with trivial valuation, our for”