Verma modules over p-adic Arens-Michael envelopes of reductive Lie algebras

JOURNAL OF ALGEBRA

卷:390

Article

Schmidt, Tobias

关键词: p-Adic number theory;    Representation theory;    Lie algebras;    BGG theory;   

DOI  :  10.1016/j.jalgebra.2013.04.038

来源: Elsevier

【 摘 要 】

Let K be a locally compact p-adic field, g a split reductive Lie algebra over K and U(g) its universal enveloping algebra. We investigate the category C-g of coadmissible modules over the p-adic Arens-Michael envelope (U) over cap (g) of U(2). Let p subset of g be a parabolic subalgebra. The main result gives a canonical equivalence between the classical parabolic BGG category of g relative to p and a certain explicitly given highest weight subcategory of C-g. This completely clarifies the Verma module theory over (U) over cap (g). (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free