On irreducible representations of compact p-adic analytic groups

• 成果类型: Article
• 署名作者: Ardakov, Konstantin; Wadsley, Simon
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2013.178.2.3
• 发表日期: 2013
• 页码: 453-557
• 关键词: differential-operators; characteristic varieties; homogeneous spaces; Algebra; MODULES; rings; localization; frobenius

摘要

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 nonzero 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.