On the restricted Verma modules at the critical level

Abstract

We study the restricted Verma modules of an affine Kac–Moody algebra at the critical level with a special emphasis on their Jordan–Hölder multiplicities. Feigin and Frenkel conjectured a formula for these multiplicities that involves the periodic Kazhdan–Lusztig polynomials. We prove this conjecture for all subgeneric blocks and for the case of anti-dominant simple subquotients.