On the existence of infinite-dimensional generalized harish-chandra modules

TL;DR

This paper establishes a broad existence theorem for infinite-dimensional admissible modules associated with reductive Lie algebras and their subalgebras, advancing the understanding of representation theory in infinite dimensions.

Contribution

It provides a general existence result for infinite-dimensional admissible (g;k)-modules, expanding the theoretical framework of Lie algebra representations.

Findings

Proves existence of infinite-dimensional admissible modules

Applies to reductive Lie algebras and subalgebras

Enhances understanding of generalized Harish-Chandra modules

Abstract

We prove a general existence result for infinite-dimensional admissible (g;k)-modules, where g is a reductive finite-dimensional complex Lie algebra and k is a reductive in g algebraic subalgebra.