A Construction of Generalized Harish-Chandra Modules with Arbitrary Minimal k-Type
Representation Theory
2007-05-23 v1
Abstract
Let g be a semisimple complex Lie algebra and k in g be any algebraic subalgebra reductive in g. For any simple finite dimensional k-module V, we construct simple (g; k)-modules M with finite dimensional k-isotypic components such that V is a k-submodule of M and the Vogan norm of any simple k-submodule V' of M; V' not isomorphic to V, is greater than the Vogan norm of V . The (g; k)-modules M are subquotients of the fundamental series of (g; k)-modules introduced in [PZ2].
Cite
@article{arxiv.math/0603371,
title = {A Construction of Generalized Harish-Chandra Modules with Arbitrary Minimal k-Type},
author = {Ivan Penkov and Gregg Zuckerman},
journal= {arXiv preprint arXiv:math/0603371},
year = {2007}
}