Verma modules over p -adic Arens–Michael envelopes of reductive Lie algebras
Copyright policy )Verma modules over p -adic Arens–Michael envelopes of reductive Lie algebras
Let K be a locally compact nonarchimedean field, g a split reductive Lie algebra over K and U(g) its universal enveloping algebra. We study the category C_g of coadmissible modules over the nonarchimedean Arens-Michael envelope of U(g). Let p be a parabolic subalgebra of g. The main result identifies a certain explicitly given highest weight category inside C_g with the classical parabolic BGG category of g relative to p. This paper is in final form, replaces and expands the former preprint 'BGG reciprocity for p-adic Arens-Michael envelopes of semisimple Lie algebras' and appears in Journal of Algebra.
21 pages
- University of Münster Germany
Representations of Lie algebras and Lie superalgebras, algebraic theory (weights), Mathematics - Number Theory, Lie algebra, Verma module, Arens-Michael envelope, Analysis on \(p\)-adic Lie groups, \(p\)-adic field, 17B10, 20G05, 22E35, category \(\mathcal{O}\), FOS: Mathematics, coadmissible module, Number Theory (math.NT), Representation Theory (math.RT), Universal enveloping (super)algebras, Mathematics - Representation Theory
Representations of Lie algebras and Lie superalgebras, algebraic theory (weights), Mathematics - Number Theory, Lie algebra, Verma module, Arens-Michael envelope, Analysis on \(p\)-adic Lie groups, \(p\)-adic field, 17B10, 20G05, 22E35, category \(\mathcal{O}\), FOS: Mathematics, coadmissible module, Number Theory (math.NT), Representation Theory (math.RT), Universal enveloping (super)algebras, Mathematics - Representation Theory
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