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

Johannes Kübel

Vol. 269 (2014), No. 2, 371–384

DOI: 10.2140/pjm.2014.269.371

Abstract

For a restricted Verma module of an affine Kac–Moody algebra at the critical level we describe the Jantzen filtration and calculate its character. This 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 derived by Arakawa and Fiebig.

Keywords

restricted Verma modules at the critical level, Jantzen sum formula, affine Kac–Moody algebras, critical representations of affine Kac–Moody algebras, Jantzen filtration, category $\mathcal{O}$

Mathematical Subject Classification 2010

Primary: 17B10, 17B67

Milestones

Received: 28 January 2013

Revised: 15 July 2013

Accepted: 23 July 2013

Published: 26 July 2014