Jantzen sum formula for restricted Verma modules over affine Kac-Moody algebras at the critical level

TL;DR

This paper extends the Jantzen sum formula to restricted Verma modules over affine Kac-Moody algebras at the critical level, providing new insights into their structure and a novel proof of the linkage principle.

Contribution

It introduces a Jantzen sum formula for restricted Verma modules at the critical level and offers a new proof of the linkage principle.

Findings

Describes the Jantzen filtration for restricted Verma modules.

Provides an alternating sum formula analogous to the baby Verma modules.

Offers a new proof of the linkage principle.

Abstract

For a restricted Verma module of an affine Kac-Moody algebra at the critical level we describe the Jantzen filtration and give an alternating sum formula which corresponds to the Jantzen sum formula of a baby Verma module over a modular Lie algebra. This also implies a new proof of the linkage principle which was already deduced by Arakawa and Fiebig.