Representations of solvable Lie algebras with filtrations

TL;DR

This paper develops a representation theory framework for solvable Lie algebras with filtrations, classifying irreducible representations and analyzing spectra of certain reducible cases.

Contribution

It introduces a new approach to represent solvable Lie algebras with filtrations, providing classification and spectral analysis.

Findings

Classification of irreducible representations achieved

Spectra of some reducible representations determined

Framework extends understanding of solvable Lie algebra representations

Abstract

We construct representation theory of Lie algebras with filtrations. In this framework a classification of irreducible representations is obtained and spectra of some reducible representations are found.