The Category of reduced imaginary Verma modules

TL;DR

This paper investigates a category analogous to category O for affine Lie algebras with zero central charge, demonstrating its semisimplicity and identifying reduced imaginary Verma modules as simple objects, generalizing prior results.

Contribution

It introduces and analyzes a new category for affine Lie algebras, extending known results from affine sl(2) to arbitrary affine Lie algebras.

Findings

The category is semisimple.

Reduced imaginary Verma modules are the simple objects.

Generalization of previous affine sl(2) results.

Abstract

For an arbitrary affine Lie algebra we study an analog of the category O for the natural Borel subalgebra and zero central charge. We show that such category is semisimple having the reduced imaginary Verma modules as its simple objects. This generalizes the result of Cox, Futorny, Misra in the case of affine sl(2).