Indecomposable generalized weight modules over the algebra of polynomial integro-differential operators

TL;DR

This paper classifies all indecomposable, generalized weight modules of finite length over the algebra of polynomial integro-differential operators, revealing their structure and Ext-group properties.

Contribution

It provides a complete classification of indecomposable generalized weight modules over the algebra of polynomial integro-differential operators, including Ext-group computations.

Findings

All such modules are infinite dimensional uniserial modules.

Ext-groups between these modules are finite dimensional vector spaces.

Abstract

For the algebra L= K <x, d/dx, \int> of polynomial integro-differential operators over a field K of characteristic zero, a classification of indecomposable, generalized weight L-modules of finite length is given. Each such module is an infinite dimensional uniserial module. Ext-groups are found between indecomposable generalized weight modules, it is proven that they are finite dimensional vector spaces.